You borrowed 10000 to be repaid over the next 5 years at 4 i

You borrowed $10,000 to be repaid over the next 5 years, at 4% interest compounded monthly. How much will you still owe after 24 monthly payments?

Solution

Step 1: Calculation of Monthly Payment Amount

Equated Monthly Installment(EMI) = Amount of Loan / Present Value Annuity Factor(r%Per Month, n*12 periods)

Where r = monthly rate of interest, n = time(in years), Present Value Annuity Factor : To be seen from Annuity Table

EMI = 10000/PVAF(4%,60)

      =10000/22.62349

      =442/-

Step 2 : Calculation of Remaining Balance after 24 Monthly Payments(Principal Amount)

Remaining Amount = Loan Amount(1+r)ⁿ - Installment Amount[((1+r)ⁿ-1)/r)]

Where, r = Interest Rate(Monthly), n = No. of installments already paid

Remaining Amount = 10000(1+0.04)²⁴   - 442[((1+0.04)²⁴ - 1)/0.04)]

                                =10000*2.5633 - 442(1.5633/.04)

                                =25633 - 17274

                                =8359/-