Question

Suppose you found a CD that pays 2.1% interest compounded monthly for 6 years. If you deposit $12,000 now, how much will you have in the account in 6 years? (Rounded to the nearest cent.) What was the interest earned? Now suppose that you would like to have $20,000 in the account in 6 years. How much would you need to deposit now?

Answer 1

The interest earned is the difference between the initial amount that was deposited in the bank and the amount that is in the account after six years.

$\begin{gathered} A\text{ = 12000\lparen1+}\frac{2.1\%}{12})^{6*12} \\ This\text{ is from the compound interest formula.} \\ A\text{ = 13609.89} \end{gathered}$

Amount in the account: $13609.89

The interest earned is therefore: 13609.89 - 12000 = $1609.89

$\begin{gathered} 20000\text{ = P\lparen1+}\frac{2.1\%}{12})^6*12 \\ 17634.24\text{ = P} \end{gathered}$

To earn $20000 in six years he should invest $17634.24.