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 $100,000 on March 28, 2039, but investors would receive nothing until then. Investors paid RBMCC $23,999 for each of these securities; so they gave up $23,999 on March 28, 2008, for the promise of a $100,000 payment 31 years later.

Based on the $23,999 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))

Suppose that, on March 28, 2018, this security’s price is $42,280. If an investor had purchased it for $23,999 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))

If an investor had purchased the security at market on March 28, 2018, 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))

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 $100,000 on March 28, 2039, but investors would receive nothing until then. Investors paid RBMCC $23,999 for each of these securities; so they gave up $23,999 on March 28, 2008, for the promise of a $100,000 payment 31 years later.

Explanation / Answer

Sol A) The rate at which RBMCC will borrow $23,999 on March 28, 2008 .RBMCC promised to repay the owner of one of these securities $100,000 on March 28, 2039, but investors would receive nothing until then. so using this our present value is $23,999 future value is $100,000 annual payment is 0 time period is 31 years .

using the formula to compute rate of return i= [(fv/pv)^1/n]-1

where i= rate of interest fv = future value pv=present value n = no of periods

i= [($100,000/$23,999)^1/31]-1

= [$4.1668^1/31 ]-1

= 1.0472-1   

= 0.0472 = 4.72%

here rate of return is 4.72%

B)   If an investor had purchased it for $23,999 at the offering and sold it on March 28, 2018, for $42,280 . then n = 10yerars

using the formula to compute rate of return i= [(fv/pv)^1/n]-1

where i= rate of interest fv = future value pv=present value n = no of periods

   i= [($42,280/$23,999)^1/10]-1

i = [$1.7617^1/10]-1

i = 1.0583 -1

= 0.0583 = 5.83%

  here the annual rate of return is 5.83%

C) An investor had purchased the security at market on March 28, 2018,for $42,280 and held it until it matured for $100,000 then n= 18years

using the formula to compute rate of return i= [(fv/pv)^1/n]-1

where i= rate of interest fv = future value pv=present value n = no of periods

   i= [($100,000/$42,280)^1/21]-1

i= [$2.3652^1/21] -1

= 1.0418 -1

= 0.0418 = 4.18%

     here the annual rate of return is 4.18%

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