Question

Rust Bucket Motor Credit Corporation (RBMCC), a subsidiary of Rust Bucket Motor, offered some securities for sale to the public on March 28, 2,006. Under the terms of the deal, RBMCC promised to repay the owner of one of these securities $84,676 on March 28, 2,039, but investors would receive nothing until then. Investors paid RBMCC $24,425 for each of these securities; so they gave up $24,425 on March 28, 2,006, for the promise of a $84,676 payment in 2,039. Suppose that, on March 28, 2,018, this security’s price is $51,204. If an investor had purchased it for $24,425 at the offering and sold it on this day, what annual rate of return would she have earned?

Answer 1

All amounts are in $

Period of holding = From March 28, 2006 to March 28, 2018 = 12 years

Purchase amount = 24,425

Sale value = 51,204

Let us see how many times the investment has grown in these 12 years

= 51,204/24,425

= 2.0963767

Annual Return may be expressed in two terms

A) Simple annual rate of return

B) Compound annual rate of return (This is preferably the best one)

B) Compounded annual rate of return

At what rate, the future value factor be equal to 2.09637 for 12 years

We can find this by using 2 methods

1. Trial and error of different rates using calculator

2. Using formula : (1+r)ⁿ = 2.09637

The answer will be the Compounded annnual rate of return = 6.3626%

A) Simple annual rate of return

Increase in investment value = (51,204-24,425)/24,425 x 100

= 109.6367%

Simple Annual return = 109.6367%/12 = 9.1365%