Question

A loan is to be repaid with level installments payable at the end of each halfyear
for 3.5 years, at a nominal rate of interest of 8% convertible semiannually.
After the fourth payment the outstanding loan balance is 5,000. Find the
initial amount of the loan.

Answer should be: $10,814.16

Answer 1

Interest Rate = 8% semi-annually

Time Period = 3.5 years = 7 periods

After 4th payment, loan Balance = $5,000

Calculating Semi-annual payment using value after 4th payment,

Using TVM Calculation,

PMT = [FV = 0, PV = 5,000, T = 3, I = 0.08/2]

PMT = $1,801.74

So,

Semi-annual payment = $1,801.74

Now calculating Initial Value of Loan using Semi-annual Payment,

Using TVM Calculation,

PV = [FV = 0, PMT = 1801.74, T = 7, I = 0.08/2]

PV = $10,814.16

So,

Initial Loan Amount = $10,814.16