Question

Mark and Kate are establishing a fund for their son's college education. They would like $60,000 in the fund at the end of 10 years. What lump sum must they deposit in an account that has an 8% annual interest rate and interest is compounded monthly? Round to the nearest cent

Answer 1

Answer:

The lump sum amount to be deposited should be $27,020.67

Explanation:

Data provided in the question:

Future value = $60,000

Time, t = 10 years

Interest rate, r = 8% = 0.08

Compounded monthly i.e number of periods n = 12

Now,

Future value = Amount deposited ×  $\left( 1 + \frac{r}{n} \right)^{\Large{n \times t}}$

Therefore,

on substituting the respective values, we get

$60,000 = Amount deposited ×  $\left( 1 + \frac{0.08}{12} \right)^{\Large{12 \times 10}}$

or

$60,000 = Amount deposited × ( 1.00667 )¹²⁰

or

$60,000 = Amount deposited × 2.220522

or

Amount deposited = $60,000 ÷ 2.220522

or

Amount deposited = $27,020.67

Hence,

The lump sum amount to be deposited should be $27,020.67