Question

n March 2015, Daniela Motor Financing (DMF), offered some securities for sale to the public. Under the terms of the deal, DMF promised to repay the owner of one of these securities $5,000 in March 2040, but investors would receive nothing until then. Investors paid DMF $2,150 for each of these securities; so they gave up $2,150 in March 2015, for the promise of a $5,000 payment 25 years later. a. Assuming you purchased the bond for $2,150, what rate of return would you earn if you held the bond for 25 years until it matured with a value $5,000?

Rate of return %?

b. Suppose under the terms of the bond you could redeem the bond in 2027. DMF agreed to pay an annual interest rate of 1.1 percent until that date. How much would the bond be worth at that time?

Bond value $?

c. In 2027, instead of cashing in the bond for its then current value, you decide to hold the bond until it matures in 2040. What annual rate of return will you earn over the last 13 years?

Rate of return %?

Answer 1

Given
Present Value (PV)	2150	Future value (FV)	5000
Period	25	yrs
Rate of return	?
Solution:
a)
Rate of return =	(FV /   PV) (1/No. of years)        - 1
=	(5000 / 2150) (1/25)       - 1
Rate of Return =	3.43%
b)	Suppose you could redeem the bond in 2027. annual interest rate of 1.1
	Therefore, n =	2027 yrs less 2015 yrs
	n =	12
FV=	Present value * (1+r)n
=	2150 * (1+1.1%)12
FV =	$2,451.62
c)	PV = 2451.62, FV=5000, n=13, Rate=?
Rate of return =	(FV /   PV) (1/No. of years)        - 1
=	(5000 / 2451.62) (1/13)       - 1
Rate of Return =	5.63%