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DFI 501: FINANCIAL MANAGEMENT

TIME VALUE OF MONEY

Amortizing a Loan

An important application of discounting and compounding concepts is in determining the payments required for an installment – type loan. The distinguishing features of this loan is that it is repaid in equal periodic (monthly, quarterly, semiannually or annually) payments that include both interest and principal. Such arrangements are prevalent in mortgage loans, auto loans, consumer loans etc.

Amortization Schedule.

An amortization schedule is a table showing the timing of payment of interest and principal necessary to pay off a loan by maturity.

Example

Determine the equal end of the year payment necessary to amortize fully a Sh.600,000, 10% loan over 4 years. Assume payment is to be rendered (i) annually, (ii) semi-annually.

Solution

(i) Annual repayments

First compute the periodic payment using Equation PMT = PVAn /PVIFAk,n.

Using tables we find the PVIFA10%,4yrs = 3.170, and we know that PVAn = Sh.600,000

PMT =600,000/3.170 = Sh.189, 274 per year.

Loan Amortization schedule

| | | | Payments | |End of year |Loan payment |Beg. Of year |Interest |Principal |End of year | | | |principal | | |principal. | | | | |[10%x (2)] |[ (1) – (3) |[ (2) – (4)] | | |(1) |(2) |(3) |(4) |(5) | |1 |189,274 |600,000 |60,000 |129,274 |470,726 | |2 |189,274 |470726 |47,073 |142,201 |328,525 | |3 |189,274 |328525 |32,853 |156,421 |172,104 | |4 |189,274 |172104 |17,210 |172,064 |- |

(ii) Semi-annual repayments

For semi-annual repayments the number of periods, n, is 8 and the discount rate is 5%.

Lets compute the periodic payment using Equation

PMT = PVAn /PVIFAk,n.

Using tables we find the PVIFA5%,8periods =6.4632, and we know that PVAn = Sh.600,000

PMT =600,000/6.4632 = Sh.92,833 per year.

Loan Amortization schedule

| | | | Payments | |End of period |Loan payment |Beg. Of year |Interest |Principal |End of period | |(6months) | |principal | | |principal. | | | | |[5%x (2)] |[ (1) – (3) |[ (2) – (4)] | | |(1) |(2) |(3) |(4) |(5) | |1 |92833 |600,000 |30,000 |62,833 |537,167 | |2 |92,833 |537,167 |26,858 |65,975 |471,192 | |3 |92,833 |471,192 |23,559 |69,274 |401918 | |4 |92,833 |401, 918 |20,096 |72,737 |329,181 | |5 |92,833 |329,181...
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