Question

Robert recently discovered a forgotten student loan bill. The amount due after 10 years is

now $10,819.33. He found some old statements and determined that after 7 years the bill

was $8831.80 and after 5 years he owed $7714.03.


1. How much did Robert borrow initially?

2. Robert is planning to pay the loan in full next year. How much will he owe then?

3. What is the interest rate on Robert’s loan?

Answer 1

1.Robert borrowed $ 5,500.00

2.The amount Robert would repay next year is $ 11,576.69

3.The interest rate on the loan is 7%

Explanation:

The interest on the loan can be computed using compound annual growth

rate

CAGR=(EB/BB)^1/n-1

EB is ending balance of $8831.80 in year7

BB is the balance of year 5 $7714.03

n=7-5=2

CAGR=(8831.8/7714.03)^(1/2)-1

CAGR==1.070000427-1

CAGR=0.070000427

CAGR=7%

The amount borrowed can be computed using the PV formula

At year 0 year 5 amount of $7714.03 is the future value

rate of interest is 7%

number of years is 5

PV=$7714.03*(1+7%)^-5

PV=$ 5,500.00

The amount Robert would pay next year is :

FV=$10,819.338(1+7%)^1

FV=$ 11,576.69