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.
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
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