Question

Mr Ismail borrowed a sum of RM 130,000 to buy a property on the following terms. Rate of interest (yield rate) =6.5%; Loan years 20; Repayable monthly for 240 months. He regularly repaid the loan already for 140 months. Now he has a huge sum of money from his grand father, which he wants to utilize it for making balloon payment of this loan. Calculate amount repayable to the bank, if the bank agreed for this proposal.

Answer 1

Amount borrowed (P) = 130,000

Rate of Interest (r) = 6.5% which is 0.54% per month

Repayment in 240 (n) months

Monthly payment: [P * r * (1 + r)^ⁿ] / [(1 + r)^ⁿ - 1] = [130,000 * 0.0054 * (1 + 0.0054)^²⁴⁰] / [(1 + 0.0054)^²⁴⁰ - 1] = 969.2451

Now he wants to clear the loan after 140 months, we will calculate the principal amount paid in 140 EMIs by calculating their present value.

Present value of first EMI: [969.2451 / 1.0054)^²⁴⁰]

Present value of second EMI: [969.2451 / 1.0054)^²³⁹]

Present value of third EMI: [969.2451 / 1.0054)^²³⁸]

and so on...

Present value of 140th EMI: [969.24 / 1.0054)^¹⁰¹]

Sum of this present value is calculated using G.P. whose formula is [a * (1 - r^ⁿ) / (1 - r)]

where a = [969.2451 / 1.0054)^²⁴⁰]

r (ratio of two consecutive terms) = 1.0054

n = 140

Sum of G.P. = {[969.2451 / 1.0054)^²⁴⁰] * (1 - 1.0054^¹⁴⁰) / (1 - 1.0054)]} = 55,316.62

Principal left = 130,000 - 55,316.62 = 74,687.37

Thus, Ismail have to pay 74,687.37 after making 140 payments.