# Sinking fund question

• Mar 9th 2008, 05:51 AM
BrainMan
Sinking fund question
I have this question I can't figure out:

\$1000 is borrowed for 20 years at 5% effective. The borrower does not pay interest currently and will pay all accrued interest at the end of 20 years together with the principal. (a) Find the total annual sinking fund deposit necessary to liquidate the loan at the end of 20 years if the sinking fund earns 4% effective. (b) Find the total annual amortization payment at 5% effective.

The annual interest payment will obviously be (1000)(.05) = 50.
These payments will accumulate according to an annuity-immediate with time = 20 and i = .05. Thus, these accumulate to (50)[((1.05)^20) - 1)/.05) = 1653.30. I just don't see what I do now.

I'm in a university-level first-year interest class and I'm studying for an exam. Would someone mind showing me how to do this problem? I have more done, but it's tough to show on the computer. I understand all the formulas, so any help doesn't have to be completely worked out.

• Mar 11th 2008, 08:55 PM
mathceleb
Quote:

Originally Posted by BrainMan
I have this question I can't figure out:

\$1000 is borrowed for 20 years at 5% effective. The borrower does not pay interest currently and will pay all accrued interest at the end of 20 years together with the principal. (a) Find the total annual sinking fund deposit necessary to liquidate the loan at the end of 20 years if the sinking fund earns 4% effective. (b) Find the total annual amortization payment at 5% effective.

The annual interest payment will obviously be (1000)(.05) = 50.
These payments will accumulate according to an annuity-immediate with time = 20 and i = .05. Thus, these accumulate to (50)[((1.05)^20) - 1)/.05) = 1653.30. I just don't see what I do now.

As promised on PM, I built this tonight for you.

You have a good start. The Total Payment on a Sinking Fund Loan is the Sinking Fund Deposit + Interest on the Loan. The 50 dollars per annum is the Interest on the Loan Payment. To see the math, let's go here:
Sinking Fund Repayment of a Loan

Press Calculate Total Payment. 4 is your sinking fund rate, 1000 is your loan amount, 20 is your term, and 5 is your effective rate. This gets us a total payment of 83.58. As you can see, 50 is for your interest paid, and 33.58 is your sinking fund deposit.

Therefore, if I'm reading your question A and B right, a = 33.58 and b = 50.

However, I've seen similar questions like yours when they say amortization method, they want to calculate the payment under the amortization method. IF that is the case and I misread your question, go here for part (b) answer:

Annuity Immediate Present Value

Calculate Payment: 5 for interest rate, 1000 for loan, 20 for term. Annual Payment is 80.24. This would make sense that it is a bit lower since the interest paid on the loan under the sinking fund method is less than our loan.

Let me know if you have questions.