Question

In 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 2045, but investors would receive nothing until then. Investors paid DMF $1,790 for each of these securities; so they gave up $1,790 in March 2015, for the promise of a $5,000 payment 30 years later.

a. Assuming you purchased the bond for $1,790, what rate of return would you earn if you held the bond for 30 years until it matured with a value $5,000? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

b. Suppose under the terms of the bond you could redeem the bond in 2027. DMF agreed to pay an annual interest rate of 1.3 percent until that date. How much would the bond be worth at that time? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

c. In 2027, instead of cashing in the bond for its then current value, you decide to hold the bond until it matures in 2045. What annual rate of return will you earn over the last 18 years?

Answer 1

This question is an application of the basic time value of money concept, which is mathematically shown as:

where PV is the present value, FV is the future value, r is the rate of interest, n is the number of years

a. In this part, PV = $1790, FV = $5000, n = 30 years, r = ?

5000 = 1790 * (1 + r)³⁰

2.7933 = (1 + r)³⁰

1.0348 = 1 + r

r = 3.48%

b. FV = ?, when PV = $1790, r = 1.3%, n = 12

FV = 1790 * (1 + 1.3%)¹²

FV = 1790 * 1.1676

FV = $2090.10

c. In this, FV = $5000, PV = $2090.1, n = 18, r =? {Since we need to calculate the rate of interest for last 18 years, when the price of bond, we calculated in part b is $2090.1

5000 = 2090.1 * (1 + r)¹⁸

1.0497 = 1 + r

=> r = 4.97%