Question

you would like to have $30,000 in an account after five years time. if the account earns 3% compounded interest yearly, what is the minimum you would need to deposit today to reach your goal? $28,092 $25,879 $29,126 $26,087

Explanation:

Step1: Recall Compound Interest Formula

The formula for compound interest to find the present value (PV) is \( PV=\frac{FV}{(1 + r)^n} \), where \( FV \) is the future value, \( r \) is the annual interest rate (in decimal), and \( n \) is the number of years.
Here, \( FV = 30000 \), \( r=0.03 \) (since 3% = 0.03), and \( n = 5 \).

Step2: Substitute Values into Formula

Substitute the values into the formula: \( PV=\frac{30000}{(1 + 0.03)^5} \).
First, calculate \( (1 + 0.03)^5 \). \( 1.03^5\approx1.159274 \).
Then, \( PV=\frac{30000}{1.159274}\approx25879 \).

Answer:

\( \$25,879 \) (the option with $25,879$)