Question

A company borrows $35000 at 14.75% simple interest from State Bank to purchase equipment. State Bank requires the company to make monthly interest-only payments and pay the full $35000 at the end of 10 years. In order to meet the 10 year obligation of $35000,the company makes equal deposits at the end of each month into a sinking fund with Wolf Savings. The sinking fund earns 6.75% compounded monthly. Note: This problem is set to allow for an answer of a specific tolerance. Be careful in your rounding. You may get some answers correct but not be in the range of answers for the others.

a. State the monthly interest payment to State Bank (rounded normally to the next cent).

b. State the amount of the equal monthly deposits to Wolf Savings, rounded normally to the next cent.

c. State the sinking fund balance at the end of 8 years.

d. State the total amount of interest earned on the sinking fund at the end of 8 years.

Answer 1

(a)

Given Loan Amount = 35,000$

Rate = 14.75% simple interest

Monthly Interest payment = Loan Amount * Rate * 1/12

= 35000*14.75%*1/12

= 430.2083 $

(b)

Sinking Fund rate (r)= 6.75%

Future value Annuity that need to be paid after 10 years = 35000

Number of years(n) = 10 years

Frequency of payments (m) = monthly = 12

Future Value Annuity = Annuity *{((1+(r/m))^(m*n) - 1 ) / (r/m)}

35000 = Annuity *{((1+(0.0675/12))^(12*10) - 1 ) / (0.0675/12)}

35000 = Annuity * 170.7239

Monthly Annuity = 35000/170.7239 = 205.0094 $

(c)

At the end of 8 years that means (8*12) = 96 months the balance would be

Future Value Annuity = Annuity *{((1+(r/m))^(m*n) - 1 ) / (r/m)}

Sinking Fund rate (r)= 6.75%

Number of years(n) = 8years

Frequency of payments (m) = monthly = 12

Annuity = 205.0094$

Future Value Annuity = 205.0094*{((1+(0.0675/12))^(12*8) - 1 ) / (0.0675/12)}

= 205.0094*126.8289

= 26,001.1098$

(d)

Amount that has been invested so far for 96 months = 205.0094*96 = 19680.9024$

Interest that has been earned = Future Value Annuity - mount that has been invested so far for 96 months

= 26001.1098 - 19680.9024

= 6320.2074$