Compound Interest worksheet

1. Future value: $46,830.18

1. Split the yearly rate into 12 parts, because interest is added 12 times a year

   $\frac{0.06}{12}$$=0.005$

2. Grow your starting deposit: add that interest 12 × 9 = 108 times, each time on the bigger balance

   $\mathrm{\$14,000.00}\times {\left(1+0.005\right)}^{12\times 9}$$=\mathrm{\$23,991.79}$

3. Find the monthly rate, i, that gives the same yearly growth. Your monthly deposits grow at this rate

   $i$$=0.005$

4. Add up your 108 monthly deposits, each with the interest it has earned

   $\mathrm{\$160.00}\times \frac{{\left(1+0.005\right)}^{108}-1}{0.005}$$=\mathrm{\$22,838.38}$

5. Add your grown starting deposit and your grown monthly deposits

   $\mathrm{\$23,991.79}+\mathrm{\$22,838.38}$$=\mathrm{\$46,830.18}$

6. Find the interest you earned: your final balance minus everything you put in

   $\mathrm{\$46,830.18}-\mathrm{\$31,280.00}$$=\mathrm{\$15,550.18}$

7. Find the yearly yield (APY): how much your money really grows in one year, with compounding counted

   ${\left(1+0.005\right)}^{12}-1\times 100$$=\mathrm{6.1678\%}$

8. Find how many years one deposit takes to double. The ln (natural log) button works the growth backward

   $\frac{\ln 2}{\ln \left(1.06167781\right)}$$=11.58$

2. Future value: $56,649.21

1. Split the yearly rate into 4 parts, because interest is added 4 times a year

   $\frac{0.05}{4}$$=0.0125$

2. Grow your starting deposit: add that interest 4 × 12 = 48 times, each time on the bigger balance

   $\mathrm{\$6,750.00}\times {\left(1+0.0125\right)}^{4\times 12}$$=\mathrm{\$12,253.65}$

3. Find the monthly rate, i, that gives the same yearly growth. Your monthly deposits grow at this rate

   $i$$=0.00414943$

4. Add up your 144 monthly deposits, each with the interest it has earned (added at the start of each month)

   $\mathrm{\$225.00}\times \frac{{\left(1+0.00414943\right)}^{144}-1}{0.00414943}\times \left(1+0.00414943\right)$$=\mathrm{\$44,395.57}$

5. Add your grown starting deposit and your grown monthly deposits

   $\mathrm{\$12,253.65}+\mathrm{\$44,395.57}$$=\mathrm{\$56,649.21}$

6. Find the interest you earned: your final balance minus everything you put in

   $\mathrm{\$56,649.21}-\mathrm{\$39,150.00}$$=\mathrm{\$17,499.21}$

7. Find the yearly yield (APY): how much your money really grows in one year, with compounding counted

   ${\left(1+0.00414943\right)}^{12}-1\times 100$$=\mathrm{5.0945\%}$

8. Find how many years one deposit takes to double. The ln (natural log) button works the growth backward

   $\frac{\ln 2}{\ln \left(1.05094534\right)}$$=13.95$

3. Future value: $40,189.16

1. Split the yearly rate into 2 parts, because interest is added 2 times a year

   $\frac{0.05}{2}$$=0.025$

2. Grow your starting deposit: add that interest 2 × 8 = 16 times, each time on the bigger balance

   $\mathrm{\$8,000.00}\times {\left(1+0.025\right)}^{2\times 8}$$=\mathrm{\$11,876.04}$

3. Find the monthly rate, i, that gives the same yearly growth. Your monthly deposits grow at this rate

   $i$$=0.00412392$

4. Add up your 96 monthly deposits, each with the interest it has earned (added at the start of each month)

   $\mathrm{\$240.00}\times \frac{{\left(1+0.00412392\right)}^{96}-1}{0.00412392}\times \left(1+0.00412392\right)$$=\mathrm{\$28,313.11}$

5. Add your grown starting deposit and your grown monthly deposits

   $\mathrm{\$11,876.04}+\mathrm{\$28,313.11}$$=\mathrm{\$40,189.16}$

6. Find the interest you earned: your final balance minus everything you put in

   $\mathrm{\$40,189.16}-\mathrm{\$31,040.00}$$=\mathrm{\$9,149.16}$

7. Find the yearly yield (APY): how much your money really grows in one year, with compounding counted

   ${\left(1+0.00412392\right)}^{12}-1\times 100$$=\mathrm{5.0625\%}$

8. Find how many years one deposit takes to double. The ln (natural log) button works the growth backward

   $\frac{\ln 2}{\ln \left(1.050625\right)}$$=14.04$

4. Future value: $75,744.84

1. Split the yearly rate into 2 parts, because interest is added 2 times a year

   $\frac{0.06}{2}$$=0.03$

2. Grow your starting deposit: add that interest 2 × 12 = 24 times, each time on the bigger balance

   $\mathrm{\$14,000.00}\times {\left(1+0.03\right)}^{2\times 12}$$=\mathrm{\$28,459.12}$

3. Find the monthly rate, i, that gives the same yearly growth. Your monthly deposits grow at this rate

   $i$$=0.00493862$

4. Add up your 144 monthly deposits, each with the interest it has earned (added at the start of each month)

   $\mathrm{\$225.00}\times \frac{{\left(1+0.00493862\right)}^{144}-1}{0.00493862}\times \left(1+0.00493862\right)$$=\mathrm{\$47,285.72}$

5. Add your grown starting deposit and your grown monthly deposits

   $\mathrm{\$28,459.12}+\mathrm{\$47,285.72}$$=\mathrm{\$75,744.84}$

6. Find the interest you earned: your final balance minus everything you put in

   $\mathrm{\$75,744.84}-\mathrm{\$46,400.00}$$=\mathrm{\$29,344.84}$

7. Find the yearly yield (APY): how much your money really grows in one year, with compounding counted

   ${\left(1+0.00493862\right)}^{12}-1\times 100$$=\mathrm{6.09\%}$

8. Find how many years one deposit takes to double. The ln (natural log) button works the growth backward

   $\frac{\ln 2}{\ln \left(1.0609\right)}$$=11.72$

5. Future value: $39,792.56

1. Grow your starting deposit with interest added all the time. The math uses e, a fixed number about 2.718

   $\mathrm{\$10,000.00}\times e^{0.05\times 10}$$=\mathrm{\$16,487.21}$

2. Find the monthly rate, i, that gives the same yearly growth. Your monthly deposits grow at this rate

   $i$$=0.00417536$

3. Add up your 120 monthly deposits, each with the interest it has earned

   $\mathrm{\$150.00}\times \frac{{\left(1+0.00417536\right)}^{120}-1}{0.00417536}$$=\mathrm{\$23,305.35}$

4. Add your grown starting deposit and your grown monthly deposits

   $\mathrm{\$16,487.21}+\mathrm{\$23,305.35}$$=\mathrm{\$39,792.56}$

5. Find the interest you earned: your final balance minus everything you put in

   $\mathrm{\$39,792.56}-\mathrm{\$28,000.00}$$=\mathrm{\$11,792.56}$

6. Find the yearly yield (APY): how much your money really grows in one year, with compounding counted

   ${\left(1+0.00417536\right)}^{12}-1\times 100$$=\mathrm{5.1271\%}$

7. Find how many years one deposit takes to double. The ln (natural log) button works the growth backward

   $\frac{\ln 2}{\ln \left(1.0512711\right)}$$=13.86$

6. Future value: $35,339.84

1. Split the yearly rate into 2 parts, because interest is added 2 times a year

   $\frac{0.03}{2}$$=0.015$

2. Grow your starting deposit: add that interest 2 × 9 = 18 times, each time on the bigger balance

   $\mathrm{\$10,000.00}\times {\left(1+0.015\right)}^{2\times 9}$$=\mathrm{\$13,073.41}$

3. Find the monthly rate, i, that gives the same yearly growth. Your monthly deposits grow at this rate

   $i$$=0.00248452$

4. Add up your 108 monthly deposits, each with the interest it has earned

   $\mathrm{\$180.00}\times \frac{{\left(1+0.00248452\right)}^{108}-1}{0.00248452}$$=\mathrm{\$22,266.43}$

5. Add your grown starting deposit and your grown monthly deposits

   $\mathrm{\$13,073.41}+\mathrm{\$22,266.43}$$=\mathrm{\$35,339.84}$

6. Find the interest you earned: your final balance minus everything you put in

   $\mathrm{\$35,339.84}-\mathrm{\$29,440.00}$$=\mathrm{\$5,899.84}$

7. Find the yearly yield (APY): how much your money really grows in one year, with compounding counted

   ${\left(1+0.00248452\right)}^{12}-1\times 100$$=\mathrm{3.0225\%}$

8. Find how many years one deposit takes to double. The ln (natural log) button works the growth backward

   $\frac{\ln 2}{\ln \left(1.030225\right)}$$=23.28$

7. Future value: $38,783.24

1. Grow your starting deposit with interest added all the time. The math uses e, a fixed number about 2.718

   $\mathrm{\$5,500.00}\times e^{0.06\times 12}$$=\mathrm{\$11,299.38}$

2. Find the monthly rate, i, that gives the same yearly growth. Your monthly deposits grow at this rate

   $i$$=0.00501252$

3. Add up your 144 monthly deposits, each with the interest it has earned (added at the start of each month)

   $\mathrm{\$130.00}\times \frac{{\left(1+0.00501252\right)}^{144}-1}{0.00501252}\times \left(1+0.00501252\right)$$=\mathrm{\$27,483.86}$

4. Add your grown starting deposit and your grown monthly deposits

   $\mathrm{\$11,299.38}+\mathrm{\$27,483.86}$$=\mathrm{\$38,783.24}$

5. Find the interest you earned: your final balance minus everything you put in

   $\mathrm{\$38,783.24}-\mathrm{\$24,220.00}$$=\mathrm{\$14,563.24}$

6. Find the yearly yield (APY): how much your money really grows in one year, with compounding counted

   ${\left(1+0.00501252\right)}^{12}-1\times 100$$=\mathrm{6.1837\%}$

7. Find how many years one deposit takes to double. The ln (natural log) button works the growth backward

   $\frac{\ln 2}{\ln \left(1.06183655\right)}$$=11.55$

8. Future value: $40,846.43

1. Split the yearly rate into 12 parts, because interest is added 12 times a year

   $\frac{0.05}{12}$$=0.00416667$

2. Grow your starting deposit: add that interest 12 × 8 = 96 times, each time on the bigger balance

   $\mathrm{\$12,000.00}\times {\left(1+0.00416667\right)}^{12\times 8}$$=\mathrm{\$17,887.03}$

3. Find the monthly rate, i, that gives the same yearly growth. Your monthly deposits grow at this rate

   $i$$=0.00416667$

4. Add up your 96 monthly deposits, each with the interest it has earned

   $\mathrm{\$195.00}\times \frac{{\left(1+0.00416667\right)}^{96}-1}{0.00416667}$$=\mathrm{\$22,959.40}$

5. Add your grown starting deposit and your grown monthly deposits

   $\mathrm{\$17,887.03}+\mathrm{\$22,959.40}$$=\mathrm{\$40,846.43}$

6. Find the interest you earned: your final balance minus everything you put in

   $\mathrm{\$40,846.43}-\mathrm{\$30,720.00}$$=\mathrm{\$10,126.43}$

7. Find the yearly yield (APY): how much your money really grows in one year, with compounding counted

   ${\left(1+0.00416667\right)}^{12}-1\times 100$$=\mathrm{5.1162\%}$

8. Find how many years one deposit takes to double. The ln (natural log) button works the growth backward

   $\frac{\ln 2}{\ln \left(1.0511619\right)}$$=13.89$

9. Future value: $40,168.86

1. Split the yearly rate into 1 parts, because interest is added 1 time a year

   $\frac{0.05}{1}$$=0.05$

2. Grow your starting deposit: add that interest 1 × 9 = 9 times, each time on the bigger balance

   $\mathrm{\$7,500.00}\times {\left(1+0.05\right)}^{1\times 9}$$=\mathrm{\$11,634.96}$

3. Find the monthly rate, i, that gives the same yearly growth. Your monthly deposits grow at this rate

   $i$$=0.00407412$

4. Add up your 108 monthly deposits, each with the interest it has earned (added at the start of each month)

   $\mathrm{\$210.00}\times \frac{{\left(1+0.00407412\right)}^{108}-1}{0.00407412}\times \left(1+0.00407412\right)$$=\mathrm{\$28,533.90}$

5. Add your grown starting deposit and your grown monthly deposits

   $\mathrm{\$11,634.96}+\mathrm{\$28,533.90}$$=\mathrm{\$40,168.86}$

6. Find the interest you earned: your final balance minus everything you put in

   $\mathrm{\$40,168.86}-\mathrm{\$30,180.00}$$=\mathrm{\$9,988.86}$

7. Find the yearly yield (APY): how much your money really grows in one year, with compounding counted

   ${\left(1+0.00407412\right)}^{12}-1\times 100$$=\mathrm{5\%}$

8. Find how many years one deposit takes to double. The ln (natural log) button works the growth backward

   $\frac{\ln 2}{\ln \left(1.05\right)}$$=14.21$

10. Future value: $37,301.26

1. Split the yearly rate into 12 parts, because interest is added 12 times a year

   $\frac{0.05}{12}$$=0.00416667$

2. Grow your starting deposit: add that interest 12 × 10 = 120 times, each time on the bigger balance

   $\mathrm{\$7,500.00}\times {\left(1+0.00416667\right)}^{12\times 10}$$=\mathrm{\$12,352.57}$

3. Find the monthly rate, i, that gives the same yearly growth. Your monthly deposits grow at this rate

   $i$$=0.00416667$

4. Add up your 120 monthly deposits, each with the interest it has earned (added at the start of each month)

   $\mathrm{\$160.00}\times \frac{{\left(1+0.00416667\right)}^{120}-1}{0.00416667}\times \left(1+0.00416667\right)$$=\mathrm{\$24,948.69}$

5. Add your grown starting deposit and your grown monthly deposits

   $\mathrm{\$12,352.57}+\mathrm{\$24,948.69}$$=\mathrm{\$37,301.26}$

6. Find the interest you earned: your final balance minus everything you put in

   $\mathrm{\$37,301.26}-\mathrm{\$26,700.00}$$=\mathrm{\$10,601.26}$

7. Find the yearly yield (APY): how much your money really grows in one year, with compounding counted

   ${\left(1+0.00416667\right)}^{12}-1\times 100$$=\mathrm{5.1162\%}$

8. Find how many years one deposit takes to double. The ln (natural log) button works the growth backward

   $\frac{\ln 2}{\ln \left(1.0511619\right)}$$=13.89$