Description
Question:
At 30 June 2017 PSC had a $5 million secured bank loan with a maturity of 30 June 2022 and an interest rate of 6% p.a. compounded quarterly. The scheduled repayments are $100,000 every three months with the initial $100,000 payment due on 30 June 2018 and the final $100,000 payment due on 30 June 2021. What is the amount of the final one-off repayment that is due on 30 June 2022 to fully pay off the loan?
Answer:
So in this question we need to find the PV of the payment using PV function on calculator.
Insert N = 3 x 4 = 12, I/Y = 6%/4, PMT = $100,000, Future Value = 0
=> Compute Present Value = $100,000(1 + PVAF,1.5%,12)
= $100,000(1 + 10.0711178)
= $100,000(11.0711178)
= $1,107,111.78
PVAF : present value of annuity factor
PMT : periodic deposit
Note: It is assumed that Periodic deposit (PMT) made at the beginning of each compound period
This is value on 30 June 2018. Its value in 2017 is
PV = FV / (1 + r)^n = 1,107,111.78 / (1 + 6%/4)^4 = $1,043,103.26
Value of outstanding loan = $5,000,000 – $1,043,103.26 = $3,956,896.74
Amount to be repaid in 2022 = PV x (1 + r)^n = 3,956,896.74 x (1 + 6%/4)^20 = $5,329,366.19
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