Problem

How much money should be deposited today in an account that earns $8.5 \%$ compounded monthly so that it will accumulate to $\$ 9000$ in three years? The amount of money that should be deposited is $\$$. (Round to the nearest cent.)

Solution

Step 1 :Given that the future value (FV) is \$9000, the annual interest rate (r) is 8.5\%, the number of times interest is compounded per year (n) is 12, and the time in years (t) is 3.

Step 2 :We need to find the present value (PV) that should be deposited today. This can be calculated using the formula for the present value of a compound interest, which is \( PV = \frac{FV}{(1 + \frac{r}{n})^{nt}} \).

Step 3 :Substituting the given values into the formula, we get \( PV = \frac{9000}{(1 + \frac{0.085}{12})^{12*3}} \).

Step 4 :Calculating the above expression, we get \( PV \approx 6980.52 \).

Step 5 :\(\boxed{6980.52}\) is the amount of money that should be deposited today.

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Source: https://solvelyapp.com/problems/2yyWCq2lEe/

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