Question 1
| Present value of loan | $450,000 |
| Interest rate | 8% |
| Amortization period | 5 years |
| Present value annuity factor for 5 years at 8 percent | 3.993 |
| Annual payment |
The annual payment of approximately $112,698 is reasonable given the interest rate of 8 percent over the 5-year period. The time value of money has been considered in the computation of the annual payment, and, as a result, the annual payment is reasonable.
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Question 2
| Present value of loan amount | $375,000 |
| Interest rate | 8 years |
| Period | 30 years |
| Monthly payment required for 30-year period | PMT (8%/12,30*12, -375000) =$2,751.62 |
| Monthly amortization payment for 15 years | PMT (8%/12,15*12, -375000) =$3,583.70 |
A smaller loan period increases the interest to be paid by the borrower. In this scenario, the monthly payment also increases.
Question 3
| Future value | $750,000 |
| Period | 20 years |
| Discount rate | 11% |
| Present value | $93,025.43 |
| Future value | $750,000 |
| Period | 15 years |
| Discount rate | 11% |
| Present value | $156,753.26 |
The present value has increased from $93,025.43 to $156,753.26 when the period changes from 20 years to 15 years.
Question 4
| Annual investment | $700 |
| Period | 4 years |
| rate | 6% |
| FV of annuity due | $700 * [(1 + 6%) 4 – 1] * (1 + 6%) / 6%=$3245.97 |
In annuity due, the financial settlements are made at the start of every period, while in ordinary annuities, the payments are made at the end of every period. Ordinary annuities are highly advantageous, especially when an individual is making payments.
Question 5
| Face value | $1000 |
| Coupon rate | 8.5% |
| Maturity period | 5 years |
| Semi-annual coupon payments | 0.0425*1000=$42.5 |
| Present value of semi-annual payments | |
| Present value of face value | |
| Present value of the bond | 5.65+321.97=$327.62 |
If a bond pays interest semi-annually rather than yearly, the interest will be compounded twice, and, as a result, the aggregate bond returns will rise at the end of the year.
