5 Time Value of Money Questions: Find the present value of $16,000 nine years fr

Question

5 Time Value of Money Questions:

Find the present value of $16,000 nine years from now. The interest rate is 9%. Find the present value of $9000 per year for 9 years with the first payment at the end of the first year at 14% interest. How long will it take to repay a 8% loan of $160,000 if $30,000 is paid at the end of each year. What would be the annual payment on a $350,000, 26 year loan at 13% interest. Find the value of a $1,000 bond paying $85 every six months and maturing 9 years from now if the current rate of interest is 11% compounded semiannually.

Explanation / Answer

a) PV = $16000 * PVIF(9%,9) ie. 0.460 = 16000 * 0.460 = $7360

b) PV = $9000 * PVIFA(14%, 9) = $9000 * 4.946 = $44514

c) M = P [(1 + r)^n * r] / [(1 + r)^n - 1]

30000 = 160000 (1 + 0.08)^n 0.08 / (1 + 0.08)^n - 1

=> (1.08)^n = 1.744186

taking log on both side, we get

n=7.23 or 8 years

d) x = 350000 (1.13)26  0.13 / (1.13)26  - 1 = 350000 * 23.99051 * 0.13 / 22.99051 = $47479.10

e) Bond value = c PVIFA(Dx,n) + par value PVIF(Dx,n)

= $85 * PVIFA(11%, 18) + 1000 * PVIF(11%, 18) = $85 * 7.702 + 1000 * 0.153 = $807.67

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