Question

you would like to have at least $10,000 in an account after eight years’ time. if the account earns 2.5% compounded interest yearly, what is the minimum amount you would need to deposit today? $8,333 $9,765 $8,208 $9,464

Explanation:

Step1: Recall compound interest formula

The compound interest formula for present value (PV) is $PV = \frac{FV}{(1 + r)^n}$, where $FV$ is future value, $r$ is annual interest rate, and $n$ is number of years.
Here, $FV = 10000$, $r = 0.025$ (2.5% as a decimal), $n = 8$.

Step2: Substitute values into formula

Substitute $FV = 10000$, $r = 0.025$, $n = 8$ into the formula:
$PV = \frac{10000}{(1 + 0.025)^8}$

Step3: Calculate $(1 + 0.025)^8$

First, calculate $1.025^8$. Using a calculator, $1.025^8 \approx 1.2184028998$.

Step4: Compute present value

$PV = \frac{10000}{1.2184028998} \approx 8208$.

Answer:

$8,208$ (corresponding to the option with $8,208$)