Matching Dell
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
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