Savings worksheet

1. Final balance: $44,021.81

1. Turn the yearly APY into a rate for each month. This rate i, earned 12 times, grows to exactly the APY in a year

   $i$$={\left(1+0.03\right)}^{\frac{1}{12}}-1$$=0.00246627$

2. Count how many deposits you'll make: years × deposits per year

   $8\times 12$$=96$

3. Grow your starting deposit. It earns interest every period, and that interest earns interest too

   $\mathrm{\$7,000.00}\times {\left(1+0.00246627\right)}^{96}$$=\mathrm{\$8,867.39}$

4. Grow your 96 regular deposits and add them up. Earlier deposits earn interest for longer

   $\mathrm{\$325.00}\times \frac{{\left(1+0.00246627\right)}^{96}-1}{0.00246627}$$=\mathrm{\$35,154.42}$

5. Add the two parts to get the final balance

   $\mathrm{\$8,867.39}+\mathrm{\$35,154.42}$$=\mathrm{\$44,021.81}$

6. Add up all the money you put in: your starting deposit plus every regular deposit

   $\text{total deposits}$$=\mathrm{\$38,200.00}$

7. Your interest is the final balance minus everything you put in

   $\mathrm{\$44,021.81}-\mathrm{\$38,200.00}$$=\mathrm{\$5,821.81}$

2. Final balance: $141,947.62

1. Turn the yearly APY into a rate for each two weeks. This rate i, earned 26 times, grows to exactly the APY in a year

   $i$$={\left(1+0.05\right)}^{\frac{1}{26}}-1$$=0.00187831$

2. Count how many deposits you'll make: years × deposits per year

   $12\times 26$$=312$

3. Grow your starting deposit. It earns interest every period, and that interest earns interest too

   $\mathrm{\$3,400.00}\times {\left(1+0.00187831\right)}^{312}$$=\mathrm{\$6,105.91}$

4. Grow your 312 regular deposits, made at the start of each period, and add them up. Earlier deposits earn interest for longer

   $\mathrm{\$320.00}\times \frac{{\left(1+0.00187831\right)}^{312}-1}{0.00187831}\times \left(1+0.00187831\right)$$=\mathrm{\$135,841.71}$

5. Add the two parts to get the final balance

   $\mathrm{\$6,105.91}+\mathrm{\$135,841.71}$$=\mathrm{\$141,947.62}$

6. Add up all the money you put in: your starting deposit plus every regular deposit

   $\text{total deposits}$$=\mathrm{\$103,240.00}$

7. Your interest is the final balance minus everything you put in

   $\mathrm{\$141,947.62}-\mathrm{\$103,240.00}$$=\mathrm{\$38,707.62}$

3. Final balance: $230,467.15

1. Turn the yearly APY into a rate for each week. This rate i, earned 52 times, grows to exactly the APY in a year

   $i$$={\left(1+0.03\right)}^{\frac{1}{52}}-1$$=0.0005686$

2. Count how many deposits you'll make: years × deposits per year

   $12\times 52$$=624$

3. Grow your starting deposit. It earns interest every period, and that interest earns interest too

   $\mathrm{\$4,000.00}\times {\left(1+0.0005686\right)}^{624}$$=\mathrm{\$5,703.04}$

4. Grow your 624 regular deposits, made at the start of each period, and add them up. Earlier deposits earn interest for longer

   $\mathrm{\$300.00}\times \frac{{\left(1+0.0005686\right)}^{624}-1}{0.0005686}\times \left(1+0.0005686\right)$$=\mathrm{\$224,764.11}$

5. Add the two parts to get the final balance

   $\mathrm{\$5,703.04}+\mathrm{\$224,764.11}$$=\mathrm{\$230,467.15}$

6. Add up all the money you put in: your starting deposit plus every regular deposit

   $\text{total deposits}$$=\mathrm{\$191,200.00}$

7. Your interest is the final balance minus everything you put in

   $\mathrm{\$230,467.15}-\mathrm{\$191,200.00}$$=\mathrm{\$39,267.15}$

4. Final balance: $142,689.79

1. Turn the yearly APY into a rate for each two weeks. This rate i, earned 26 times, grows to exactly the APY in a year

   $i$$={\left(1+0.05\right)}^{\frac{1}{26}}-1$$=0.00187831$

2. Count how many deposits you'll make: years × deposits per year

   $11\times 26$$=286$

3. Grow your starting deposit. It earns interest every period, and that interest earns interest too

   $\mathrm{\$7,000.00}\times {\left(1+0.00187831\right)}^{286}$$=\mathrm{\$11,972.38}$

4. Grow your 286 regular deposits, made at the start of each period, and add them up. Earlier deposits earn interest for longer

   $\mathrm{\$345.00}\times \frac{{\left(1+0.00187831\right)}^{286}-1}{0.00187831}\times \left(1+0.00187831\right)$$=\mathrm{\$130,717.42}$

5. Add the two parts to get the final balance

   $\mathrm{\$11,972.38}+\mathrm{\$130,717.42}$$=\mathrm{\$142,689.79}$

6. Add up all the money you put in: your starting deposit plus every regular deposit

   $\text{total deposits}$$=\mathrm{\$105,670.00}$

7. Your interest is the final balance minus everything you put in

   $\mathrm{\$142,689.79}-\mathrm{\$105,670.00}$$=\mathrm{\$37,019.79}$

5. Final balance: $8,791.18

1. You deposit once a year, so the rate for each year is the APY itself

   $i$$=0.04$

2. Count how many deposits you'll make: years × deposits per year

   $7\times 1$$=7$

3. Grow your starting deposit. It earns interest every period, and that interest earns interest too

   $\mathrm{\$5,000.00}\times {\left(1+0.04\right)}^7$$=\mathrm{\$6,579.66}$

4. Grow your 7 regular deposits and add them up. Earlier deposits earn interest for longer

   $\mathrm{\$280.00}\times \frac{{\left(1+0.04\right)}^7-1}{0.04}$$=\mathrm{\$2,211.52}$

5. Add the two parts to get the final balance

   $\mathrm{\$6,579.66}+\mathrm{\$2,211.52}$$=\mathrm{\$8,791.18}$

6. Add up all the money you put in: your starting deposit plus every regular deposit

   $\text{total deposits}$$=\mathrm{\$6,960.00}$

7. Your interest is the final balance minus everything you put in

   $\mathrm{\$8,791.18}-\mathrm{\$6,960.00}$$=\mathrm{\$1,831.18}$

6. Final balance: $63,198.19

1. Turn the yearly APY into a rate for each two weeks. This rate i, earned 26 times, grows to exactly the APY in a year

   $i$$={\left(1+0.04\right)}^{\frac{1}{26}}-1$$=0.00150963$

2. Count how many deposits you'll make: years × deposits per year

   $9\times 26$$=234$

3. Grow your starting deposit. It earns interest every period, and that interest earns interest too

   $\mathrm{\$5,000.00}\times {\left(1+0.00150963\right)}^{234}$$=\mathrm{\$7,116.56}$

4. Grow your 234 regular deposits and add them up. Earlier deposits earn interest for longer

   $\mathrm{\$200.00}\times \frac{{\left(1+0.00150963\right)}^{234}-1}{0.00150963}$$=\mathrm{\$56,081.63}$

5. Add the two parts to get the final balance

   $\mathrm{\$7,116.56}+\mathrm{\$56,081.63}$$=\mathrm{\$63,198.19}$

6. Add up all the money you put in: your starting deposit plus every regular deposit

   $\text{total deposits}$$=\mathrm{\$51,800.00}$

7. Your interest is the final balance minus everything you put in

   $\mathrm{\$63,198.19}-\mathrm{\$51,800.00}$$=\mathrm{\$11,398.19}$

7. Final balance: $6,861.71

1. You deposit once a year, so the rate for each year is the APY itself

   $i$$=0.05$

2. Count how many deposits you'll make: years × deposits per year

   $7\times 1$$=7$

3. Grow your starting deposit. It earns interest every period, and that interest earns interest too

   $\mathrm{\$2,750.00}\times {\left(1+0.05\right)}^7$$=\mathrm{\$3,869.53}$

4. Grow your 7 regular deposits, made at the start of each period, and add them up. Earlier deposits earn interest for longer

   $\mathrm{\$350.00}\times \frac{{\left(1+0.05\right)}^7-1}{0.05}\times \left(1+0.05\right)$$=\mathrm{\$2,992.19}$

5. Add the two parts to get the final balance

   $\mathrm{\$3,869.53}+\mathrm{\$2,992.19}$$=\mathrm{\$6,861.71}$

6. Add up all the money you put in: your starting deposit plus every regular deposit

   $\text{total deposits}$$=\mathrm{\$5,200.00}$

7. Your interest is the final balance minus everything you put in

   $\mathrm{\$6,861.71}-\mathrm{\$5,200.00}$$=\mathrm{\$1,661.71}$

8. Final balance: $49,897.90

1. Turn the yearly APY into a rate for each month. This rate i, earned 12 times, grows to exactly the APY in a year

   $i$$={\left(1+0.03\right)}^{\frac{1}{12}}-1$$=0.00246627$

2. Count how many deposits you'll make: years × deposits per year

   $10\times 12$$=120$

3. Grow your starting deposit. It earns interest every period, and that interest earns interest too

   $\mathrm{\$6,000.00}\times {\left(1+0.00246627\right)}^{120}$$=\mathrm{\$8,063.50}$

4. Grow your 120 regular deposits and add them up. Earlier deposits earn interest for longer

   $\mathrm{\$300.00}\times \frac{{\left(1+0.00246627\right)}^{120}-1}{0.00246627}$$=\mathrm{\$41,834.40}$

5. Add the two parts to get the final balance

   $\mathrm{\$8,063.50}+\mathrm{\$41,834.40}$$=\mathrm{\$49,897.90}$

6. Add up all the money you put in: your starting deposit plus every regular deposit

   $\text{total deposits}$$=\mathrm{\$42,000.00}$

7. Your interest is the final balance minus everything you put in

   $\mathrm{\$49,897.90}-\mathrm{\$42,000.00}$$=\mathrm{\$7,897.90}$

9. Final balance: $209,378.90

1. Turn the yearly APY into a rate for each week. This rate i, earned 52 times, grows to exactly the APY in a year

   $i$$={\left(1+0.04\right)}^{\frac{1}{52}}-1$$=0.00075453$

2. Count how many deposits you'll make: years × deposits per year

   $10\times 52$$=520$

3. Grow your starting deposit. It earns interest every period, and that interest earns interest too

   $\mathrm{\$3,750.00}\times {\left(1+0.00075453\right)}^{520}$$=\mathrm{\$5,550.92}$

4. Grow your 520 regular deposits, made at the start of each period, and add them up. Earlier deposits earn interest for longer

   $\mathrm{\$320.00}\times \frac{{\left(1+0.00075453\right)}^{520}-1}{0.00075453}\times \left(1+0.00075453\right)$$=\mathrm{\$203,827.99}$

5. Add the two parts to get the final balance

   $\mathrm{\$5,550.92}+\mathrm{\$203,827.99}$$=\mathrm{\$209,378.90}$

6. Add up all the money you put in: your starting deposit plus every regular deposit

   $\text{total deposits}$$=\mathrm{\$170,150.00}$

7. Your interest is the final balance minus everything you put in

   $\mathrm{\$209,378.90}-\mathrm{\$170,150.00}$$=\mathrm{\$39,228.90}$

10. Final balance: $36,193.95

1. Turn the yearly APY into a rate for each month. This rate i, earned 12 times, grows to exactly the APY in a year

   $i$$={\left(1+0.04\right)}^{\frac{1}{12}}-1$$=0.00327374$

2. Count how many deposits you'll make: years × deposits per year

   $8\times 12$$=96$

3. Grow your starting deposit. It earns interest every period, and that interest earns interest too

   $\mathrm{\$3,750.00}\times {\left(1+0.00327374\right)}^{96}$$=\mathrm{\$5,132.13}$

4. Grow your 96 regular deposits, made at the start of each period, and add them up. Earlier deposits earn interest for longer

   $\mathrm{\$275.00}\times \frac{{\left(1+0.00327374\right)}^{96}-1}{0.00327374}\times \left(1+0.00327374\right)$$=\mathrm{\$31,061.82}$

5. Add the two parts to get the final balance

   $\mathrm{\$5,132.13}+\mathrm{\$31,061.82}$$=\mathrm{\$36,193.95}$

6. Add up all the money you put in: your starting deposit plus every regular deposit

   $\text{total deposits}$$=\mathrm{\$30,150.00}$

7. Your interest is the final balance minus everything you put in

   $\mathrm{\$36,193.95}-\mathrm{\$30,150.00}$$=\mathrm{\$6,043.95}$