Question

Bucket Motor Credit Corporation (RBMCC), a subsidiary of Rust Bucket Motor, offered some securities for sale to the public on March 28, 2002. Under the terms of the deal, RBMCC promised to repay the owner of one of these securities $93714 on March 28, 2040, but investors would receive nothing until then. Investors paid RBMCC $22127 for each of these securities; so they gave up $22127 on March 28, 2002, for the promise of a $93714 payment in 2040. Based on the $22127 price, what rate was RBMCC paying to borrow money? (as a percentage and round to 2 decimal places)

Answer 1

Correct Answer = 3.87 %

Solution. Formula for calculating compound interest (A) = P(1+r/100)^t

Where A stands for amount

P stands for principle

R stands for rate

t stands for Time

A = P(1+r/100)^38

A=93714

P=22127

t= 2040-2002 = 38 years

we have to calculate the rate of interest.

$ 93714 = 22127(1+r/100)^38

93714/22127 = (1+r/100)^38

4.23527817 = (1+r/100)^38

4.23527817^(1/38) = 1+r/100 (working note given below for this step.)

1.03871617 = 1+r/100

1- 1.03871617 = r/100

.03871617 = r/100

R = .03871617 * 100

R =3.871617 %

working note

4.23527817^(1/38) = 1+r/100

in this step we have to calculate 4.325278 root 38 that's why it's raised to the power 1/38.