Question

On January 15, 2000, Enterprise A loans $6,000 to Enterprise B and $17,000 to Enterprise C. Enterprise B repays Enterprise A $7,000 on January 15, 2002 and this money is reinvested at a 5% annual effective rate. Enterprise C repays Enterprise A $22,500 on January 15, 2004. What is the annual yield received by Enterprise A over the four-year interval. Compare it to the annual effective interest rates paid by Enterprises B and C

Answer 1

A) yield for company A: 8.79

B) effective rate on the loan:

B = 8.01%

C = 7.26%

Step-by-step explanation:

A)

enterprise B interest

7000 - 6000 = 1, 000

proceed from B repayment deposit at 5%

7000 x 1.05^2 -7,000 = 717,5‬

enterprise C interest

22,500 - 17,000 = 5,500

total return 7, 217.5

principal 17,000 + 6,000 = 23,000

we need to solve for the rate of a principal of 23,000 which yield 7,217.5 interest

`Principal \: (1+ r)^(time) = Amount`

`23,000 \: (1+ r)^(time) = 30,217.5`

`\sqrt[4]{30,217.5/ 23,000} -1 = r`

r = 0.087905069

B) from the formula above we se each enterprise principal, amount and time:

effective rate for B:

`\sqrt[2]{7,000/ 6,000} -1 = r`

0.08012345

effective rate for C

`\sqrt[4]{23,500/ 17,000} -1 = r`

0.072589149