Question

Helen borrows a sum of money from a bank at 12% convertible monthly and wishes to repay it by 24 monthly payments. In total, she will pay $584 of interest. Determine the size of the loan.

Answer 1

Size of the Loan = 4500

Steps in calculation

The term convertible monthly means, compounded monthly.

Interest rate per month = 0.12 / 12 = 0.01

n = number of installments = 24

Let ........... X be the size of loan

Step - (1) ...........Define monthly installment

Now, we have, monthly installment = Size of loan / Present value of annuity

PVA = [ 1 - (1+r)^-n ] / r

= [ 1 - (1.01)^-24 ] / 0.01

= 21.2433872576

Monthly installment = X / 21.2433872576  

Step - (2) ............Define total installments paid

Total payment over 24 months = (24 * X ) / 21.2433872576

= X * 1.1297633334

Step - (3) .............Find the Loan size

Now, Principle loan amount = Total amount paid over 24 months - Interest amount

= X * 1.1297633334 - 584 = X

X * 1.1297633334 - X = 584

X * 0.1297633334 = 584

X = 584 / 0.1297633334

X = 4500