Rust Bucket Motor Credit Corporation (RBMCC), a subsidiary of Rust Bucket Motor,

Question

Rust Bucket Motor Credit Corporation (RBMCC), a subsidiary of Rust Bucket Motor, offered some securities for sale to the public on March 28, 2008. Under the terms of the deal, RBMCC promised to repay the owner of one of these securities dollar 100, 000 on March 28, 2037, but investors would receive nothing until then. Investors paid RBMCC dollar 23,799 for each of these securities; so they gave up dollar 23,799 on March 28, 2008, for the promise of a dollar 100, 000 payment 29 years later. Based on the dollar 23,799 price, what rate was RBMCC paying to borrow money? (Do not round intermediate calculations and round your final answer to 2 decimal places, (e.g., 32.16)) Rate of return percentage Suppose that, on March 28, 2020, this security's price is dollar 42,080. If an investor had purchased it for dollar 23,799 at the offering and sold it on this day, what annual rate of return would she have earned? (Do not round intermediate calculations and round your final answer to 2 decimal places, (e.g., 32.16)) Annual rate of return percentage If an investor had purchased the security at market on March 28, 2020, and held it until it matured, what annual rate of return would she have earned? (Do not round intermediate calculations and round your final answer to 2 decimal places, (e.g., 32.16)) Annual rate of return percentage

Explanation / Answer

(a)Amount Deposited=A=23799

Maturity Value=MV=100000

Period of Deposit=n=29 Years

So, MV=A*(1+r)^n , where r=Rate of return

100000=23799*(1+r)^29

or (1+r)^29=4.20=(1.0508)^29

or 1+r = 1.0508

or r=0.0508 or 5.08%

(b) 23799 that was invested in 2008 grew to become 42080 in 2020. So here n=12

So 42080=23799(1+r)^12

or (1+r)^12=42080/23799=1.768

or (1+r)^12=1.0486^12

or 1+r=1.0486

or r=0.0486 or 4.86%

(c) Here A=42080 and MV=100000 and n=17

So, 42080(1+r)^17=100000

or (1+r)^17=100000/42080= 2.376

or (1+r)^17=(1.052)^17

or (1+r)=1.052

or r=0.052 or 5.2%

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