You deposit $$ \$ 1000 $$ each year into an account earning 28 interest compounded annually. How much will y have in the account in 15 years? Submit Question

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UpStudy AI · Accepted Answer

To calculate the amount of money in the account after 15 years with annual deposits of $1000 and an annual interest rate of 28% compounded annually, we can use the formula for compound interest with periodic payments:

$$ A = P \left( \frac{(1 + r)^n - 1}{r} \right) $$

where:
- $$ A $$ is the total amount in the account after $$ n $$ years,
- $$ P $$ is the annual deposit amount,
- $$ r $$ is the annual interest rate (in decimal form),
- $$ n $$ is the number of years.

Given:
- $$ P = \$1000 $$,
- $$ r = 28\% = 0.28 $$,
- $$ n = 15 $$ years.

Substitute the values into the formula to find the total amount in the account after 15 years.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{1000\left(\left(1+0.28\right)^{15}-1\right)}{0.28}$$
- step1: Add the numbers:
  $$\frac{1000\left(1.28^{15}-1\right)}{0.28}$$
- step2: Convert the expressions:
  $$\frac{1000\left(\left(\frac{32}{25}\right)^{15}-1\right)}{0.28}$$
- step3: Subtract the numbers:
  $$\frac{1000\times \frac{32^{15}-25^{15}}{25^{15}}}{0.28}$$
- step4: Multiply the numbers:
  $$\frac{\frac{2^{78}-8\times 25^{15}}{5^{27}}}{0.28}$$
- step5: Convert the expressions:
  $$\frac{\frac{2^{78}-8\times 25^{15}}{5^{27}}}{\frac{7}{25}}$$
- step6: Multiply by the reciprocal:
  $$\frac{2^{78}-8\times 25^{15}}{5^{27}}\times \frac{25}{7}$$
- step7: Rewrite the expression:
  $$\frac{2^{78}-8\times 25^{15}}{5^{27}}\times \frac{5^{2}}{7}$$
- step8: Reduce the numbers:
  $$\frac{2^{78}-8\times 25^{15}}{5^{25}}\times \frac{1}{7}$$
- step9: Multiply the fractions:
  $$\frac{2^{78}-8\times 25^{15}}{5^{25}\times 7}$$
- step10: Multiply:
  $$\frac{2^{78}-8\times 25^{15}}{7\times 5^{25}}$$
The total amount in the account after 15 years with annual deposits of $1000 and an annual interest rate of 28% compounded annually is approximately $141,302.93.
After 15 years, you will have approximately \$141,302.93 in the account.

You deposit \( \$ 1000 \) each year into an account earning 28 interest compounded annually. How much will y have in the account in 15 years? Submit Question

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