Final answer:
To accumulate $89,000 in 13 years with an APR of 6%, you should deposit approximately $423.28 per month. You should also invest approximately $423.28 per month.
Step-by-step explanation:
To answer this question, we can use the savings plan formula which is:
A = P*(1+r)^n
Where:
- A is the future value of the investment
- P is the monthly deposit amount
- r is the monthly interest rate (APR/12)
- n is the number of months
A. In this case, we want to accumulate $89,000 in 13 years. The monthly deposit amount is P, the APR is 6% which is equivalent to a monthly interest rate of 0.06/12 = 0.005. Plugging these values into the formula, we get:
A = P*(1+0.005)^156
Next, we solve for P:
$89,000 = P*(1.005)^156
Dividing both sides by (1.005)^156, we get:
P = $89,000 / (1.005)^156 ≈ $423.28
Therefore, you should deposit approximately $423.28 per month to accumulate $89,000 in 13 years.
B. Since we already know the future value and the number of years, we can rearrange the formula to solve for P:
$89,000 = P*(1+0.005)^156
Dividing both sides by (1.005)^156, we get:
P = $89,000 / (1.005)^156 ≈ $423.28
Therefore, you should invest approximately $423.28 per month.