Question

Barbara borrows $3000. She agrees to make monthly interest payments on the loan and will build up a sinking fund with monthly deposits to repay the principal with a single payment 19 months from now. If the interest being charged on the loan is j12 = 8.5% and the interest being earned on the sinking fund is j12= 5.4%, what is the monthly cost of the debt for Barbara?

Answer 1

Solution:

The interest to the lender is based on an annual rate of 8.5%.
Using the simple interest formula, I = Prt.
We get, I = 3000 * (0.085) * (1) = 255 per year.
Dividing by 12 to get monthly interest payment = 255/12 = 21.25

The amount to be deposited in the sinking fund each month is given by following formula:
P = (Amounts need to be accumulated * Interest rate per period) / [ ((1+interest rate per period)^number of time periods) - 1]

The amount to be accumulated = Original borrowed amount = 3000
The interest being earned on the sinking fund based on annual rate is 5.4%
The interest rate per period = 5.4%% divided by 12 = 0.054/12 = 0.0045 or 0.45%.
The number of periods = 19 months.

The amount to be deposited in the sinking fund each month = (3000 * 0.0045) / [ ((1+0.0045)^19) - 1] = 135 / 0.08905 = 1515.957
So, the monthly payment into the sinking fund is $1,515.957.

The monthly cost of the debt for Barbara = The monthly payment into the sinking fund + monthly interest payment = 1515.957 + 21.25 = $1,537.207.