Future Value worksheet

1. Future value: $38,538.36

1. Find the rate for each two weeks (i): divide the yearly rate by 26, because interest is added 26 times a year

   $i$$=\frac{0.05}{26}$$=0.00192308$

2. Count the periods (N): 26 a year for 8 years

   $N$$=26\times 8$$=208$

3. Grow the starting amount, adding interest on interest every period

   $\mathrm{\$7,000.00}\times {\left(1+0.00192308\right)}^{208}$$=\mathrm{\$10,438.76}$

4. Grow each of the 208 payments for the periods it has left, and add them up

   $\mathrm{\$110.00}\times \frac{{\left(1+0.00192308\right)}^{208}-1}{0.00192308}$$=\mathrm{\$28,099.60}$

5. Add the grown starting amount and the grown payments to get the future value

   $\mathrm{\$10,438.76}+\mathrm{\$28,099.60}$$=\mathrm{\$38,538.36}$

6. Take away everything you put in to see how much interest you earned

   $\mathrm{\$38,538.36}-\mathrm{\$29,880.00}$$=\mathrm{\$8,658.36}$

2. Future value: $15,752.69

1. Find the rate for each quarter (i): divide the yearly rate by 4, because interest is added 4 times a year

   $i$$=\frac{0.07}{4}$$=0.0175$

2. Count the periods (N): 4 a year for 12 years

   $N$$=4\times 12$$=48$

3. Grow the starting amount, adding interest on interest every period

   $\mathrm{\$3,400.00}\times {\left(1+0.0175\right)}^{48}$$=\mathrm{\$7,818.64}$

4. Grow each of the 48 payments for the periods it has left, and add them up. Then multiply by (1 + i), because each is made at the start of its period

   $\mathrm{\$105.00}\times \frac{{\left(1+0.0175\right)}^{48}-1}{0.0175}\times \left(1+0.0175\right)$$=\mathrm{\$7,934.05}$

5. Add the grown starting amount and the grown payments to get the future value

   $\mathrm{\$7,818.64}+\mathrm{\$7,934.05}$$=\mathrm{\$15,752.69}$

6. Take away everything you put in to see how much interest you earned

   $\mathrm{\$15,752.69}-\mathrm{\$8,440.00}$$=\mathrm{\$7,312.69}$

3. Future value: $10,550.68

1. Find the rate for each half-year (i): divide the yearly rate by 2, because interest is added 2 times a year

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

2. Count the periods (N): 2 a year for 12 years

   $N$$=2\times 12$$=24$

3. Grow the starting amount, adding interest on interest every period

   $\mathrm{\$4,000.00}\times {\left(1+0.025\right)}^{24}$$=\mathrm{\$7,234.90}$

4. Grow each of the 24 payments for the periods it has left, and add them up. Then multiply by (1 + i), because each is made at the start of its period

   $\mathrm{\$100.00}\times \frac{{\left(1+0.025\right)}^{24}-1}{0.025}\times \left(1+0.025\right)$$=\mathrm{\$3,315.78}$

5. Add the grown starting amount and the grown payments to get the future value

   $\mathrm{\$7,234.90}+\mathrm{\$3,315.78}$$=\mathrm{\$10,550.68}$

6. Take away everything you put in to see how much interest you earned

   $\mathrm{\$10,550.68}-\mathrm{\$6,400.00}$$=\mathrm{\$4,150.68}$

4. Future value: $22,743.45

1. Find the rate for each quarter (i): divide the yearly rate by 4, because interest is added 4 times a year

   $i$$=\frac{0.07}{4}$$=0.0175$

2. Count the periods (N): 4 a year for 11 years

   $N$$=4\times 11$$=44$

3. Grow the starting amount, adding interest on interest every period

   $\mathrm{\$7,000.00}\times {\left(1+0.0175\right)}^{44}$$=\mathrm{\$15,018.01}$

4. Grow each of the 44 payments for the periods it has left, and add them up. Then multiply by (1 + i), because each is made at the start of its period

   $\mathrm{\$116.00}\times \frac{{\left(1+0.0175\right)}^{44}-1}{0.0175}\times \left(1+0.0175\right)$$=\mathrm{\$7,725.44}$

5. Add the grown starting amount and the grown payments to get the future value

   $\mathrm{\$15,018.01}+\mathrm{\$7,725.44}$$=\mathrm{\$22,743.45}$

6. Take away everything you put in to see how much interest you earned

   $\mathrm{\$22,743.45}-\mathrm{\$12,104.00}$$=\mathrm{\$10,639.45}$

5. Future value: $325,104.20

1. Find the rate for each day (i): divide the yearly rate by 365, because interest is added 365 times a year

   $i$$=\frac{0.06}{365}$$=0.00016438$

2. Count the periods (N): 365 a year for 7 years

   $N$$=365\times 7$$=\mathrm{2,555}$

3. Grow the starting amount, adding interest on interest every period

   $\mathrm{\$5,000.00}\times {\left(1+0.00016438\right)}^{\mathrm{2,555}}$$=\mathrm{\$7,609.55}$

4. Grow each of the 2555 payments for the periods it has left, and add them up

   $\mathrm{\$100.00}\times \frac{{\left(1+0.00016438\right)}^{\mathrm{2,555}}-1}{0.00016438}$$=\mathrm{\$317,494.66}$

5. Add the grown starting amount and the grown payments to get the future value

   $\mathrm{\$7,609.55}+\mathrm{\$317,494.66}$$=\mathrm{\$325,104.20}$

6. Take away everything you put in to see how much interest you earned

   $\mathrm{\$325,104.20}-\mathrm{\$260,500.00}$$=\mathrm{\$64,604.20}$

6. Future value: $11,618.64

1. Find the rate for each quarter (i): divide the yearly rate by 4, because interest is added 4 times a year

   $i$$=\frac{0.06}{4}$$=0.015$

2. Count the periods (N): 4 a year for 9 years

   $N$$=4\times 9$$=36$

3. Grow the starting amount, adding interest on interest every period

   $\mathrm{\$5,000.00}\times {\left(1+0.015\right)}^{36}$$=\mathrm{\$8,545.70}$

4. Grow each of the 36 payments for the periods it has left, and add them up

   $\mathrm{\$65.00}\times \frac{{\left(1+0.015\right)}^{36}-1}{0.015}$$=\mathrm{\$3,072.94}$

5. Add the grown starting amount and the grown payments to get the future value

   $\mathrm{\$8,545.70}+\mathrm{\$3,072.94}$$=\mathrm{\$11,618.64}$

6. Take away everything you put in to see how much interest you earned

   $\mathrm{\$11,618.64}-\mathrm{\$7,340.00}$$=\mathrm{\$4,278.64}$

7. Future value: $386,976.60

1. Find the rate for each day (i): divide the yearly rate by 365, because interest is added 365 times a year

   $i$$=\frac{0.07}{365}$$=0.00019178$

2. Count the periods (N): 365 a year for 7 years

   $N$$=365\times 7$$=\mathrm{2,555}$

3. Grow the starting amount, adding interest on interest every period

   $\mathrm{\$2,750.00}\times {\left(1+0.00019178\right)}^{\mathrm{2,555}}$$=\mathrm{\$4,488.66}$

4. Grow each of the 2555 payments for the periods it has left, and add them up. Then multiply by (1 + i), because each is made at the start of its period

   $\mathrm{\$116.00}\times \frac{{\left(1+0.00019178\right)}^{\mathrm{2,555}}-1}{0.00019178}\times \left(1+0.00019178\right)$$=\mathrm{\$382,487.94}$

5. Add the grown starting amount and the grown payments to get the future value

   $\mathrm{\$4,488.66}+\mathrm{\$382,487.94}$$=\mathrm{\$386,976.60}$

6. Take away everything you put in to see how much interest you earned

   $\mathrm{\$386,976.60}-\mathrm{\$299,130.00}$$=\mathrm{\$87,846.60}$

8. Future value: $25,410.28

1. Find the rate for each month (i): divide the yearly rate by 12, because interest is added 12 times a year

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

2. Count the periods (N): 12 a year for 10 years

   $N$$=12\times 10$$=120$

3. Grow the starting amount, adding interest on interest every period

   $\mathrm{\$6,000.00}\times {\left(1+0.00416667\right)}^{120}$$=\mathrm{\$9,882.06}$

4. Grow each of the 120 payments for the periods it has left, and add them up

   $\mathrm{\$100.00}\times \frac{{\left(1+0.00416667\right)}^{120}-1}{0.00416667}$$=\mathrm{\$15,528.23}$

5. Add the grown starting amount and the grown payments to get the future value

   $\mathrm{\$9,882.06}+\mathrm{\$15,528.23}$$=\mathrm{\$25,410.28}$

6. Take away everything you put in to see how much interest you earned

   $\mathrm{\$25,410.28}-\mathrm{\$18,000.00}$$=\mathrm{\$7,410.28}$

9. Future value: $8,252.56

1. Find the rate for each year (i): divide the yearly rate by 1, because interest is added 1 time a year

   $i$$=\frac{0.06}{1}$$=0.06$

2. Count the periods (N): 1 a year for 10 years

   $N$$=1\times 10$$=10$

3. Grow the starting amount, adding interest on interest every period

   $\mathrm{\$3,750.00}\times {\left(1+0.06\right)}^{10}$$=\mathrm{\$6,715.68}$

4. Grow each of the 10 payments for the periods it has left, and add them up. Then multiply by (1 + i), because each is made at the start of its period

   $\mathrm{\$110.00}\times \frac{{\left(1+0.06\right)}^{10}-1}{0.06}\times \left(1+0.06\right)$$=\mathrm{\$1,536.88}$

5. Add the grown starting amount and the grown payments to get the future value

   $\mathrm{\$6,715.68}+\mathrm{\$1,536.88}$$=\mathrm{\$8,252.56}$

6. Take away everything you put in to see how much interest you earned

   $\mathrm{\$8,252.56}-\mathrm{\$4,850.00}$$=\mathrm{\$3,402.56}$

10. Future value: $32,776.29

1. Find the rate for each two weeks (i): divide the yearly rate by 26, because interest is added 26 times a year

   $i$$=\frac{0.06}{26}$$=0.00230769$

2. Count the periods (N): 26 a year for 8 years

   $N$$=26\times 8$$=208$

3. Grow the starting amount, adding interest on interest every period

   $\mathrm{\$3,750.00}\times {\left(1+0.00230769\right)}^{208}$$=\mathrm{\$6,056.93}$

4. Grow each of the 208 payments for the periods it has left, and add them up. Then multiply by (1 + i), because each is made at the start of its period

   $\mathrm{\$100.00}\times \frac{{\left(1+0.00230769\right)}^{208}-1}{0.00230769}\times \left(1+0.00230769\right)$$=\mathrm{\$26,719.36}$

5. Add the grown starting amount and the grown payments to get the future value

   $\mathrm{\$6,056.93}+\mathrm{\$26,719.36}$$=\mathrm{\$32,776.29}$

6. Take away everything you put in to see how much interest you earned

   $\mathrm{\$32,776.29}-\mathrm{\$24,550.00}$$=\mathrm{\$8,226.29}$