Answer to Question #284981 in Finance for Susu

Question

imi recently inherited some bonds (face value RM100,000) from her father, and soon thereafter she became engaged to Mamat, a Universiti Teknologi MARA, investment graduate.

Mamat wants Mimi to cash in the bonds, so the two of them can use the money for two years in Monte Carlo. The 2 percent annual coupon bonds mature on January 1, 2041, and it is now January 1, 2021. Interest on these bonds is paid annually and new annual coupon bonds with similar risk and maturity are currently yielding 12 percent.

If Mimi sells her bonds today and puts the proceeds into an account which pays 10 percent compounded annually, what would be the equal annual amounts she could withdraw from the account in the said 2 years’ time (2 equal annuity withdrawal amount)

Answer 1

face value $F=100,000$

Coupon $C= 0.02*100,000=2,000$

Time to maturity $t=10 \ years$

Interest$\ r=0.12$

Present value

$$PV= C* \frac{1-(1+r)^{-t}}{r} + \frac{F}{(1+r)^t}$$ $$PV= 2,000* \frac{1-(1+0.12)^{-10}}{0.12} + \frac{100,000}{(1+0.12)^{10}}$$ $$11,300.4461 + 32,197.3237= 43,497.7698$$

She will receive 43,497.7698 from the sale of the bonds.

Investing so that she can withdraw beginning today:

$$PV= C* \frac{1-(1+r)^{-t}}{r} (1+r)$$ $$43,497.7698= C* \frac{1-(1+0.10)^{-2}}{0.10} (1+0.1)$$ $$1.9091*C=43,497.7698$$ $$C=22,784.5461$$

answer: she can make equal withdrawals of $R\ 22,784.5461$