Paying of loan in 9 months

Question

How much interest will someone pay on a loan of 10 000$ if this person paying the loan of in 9 months and the loan rate is 4%?

Which formula is suitable for this? Is 10 000$ PMT?

Answer 1

If we assume equal monthly payments will be made, you can calculate total interest paid with Excel's cumulative interest payment function, CUMIPMT.

The arguments for CUMIPMT are rate, nper, PV, start_period, end_period, and type:

1. For rate, divide the 4% rate by 12 to get the monthly interest rate (assuming the 4% is an annual rate).
2. Rate, nper, and PV must be greater than 0, so be sure to enter a positive value for the loan amount.
3. For type, use 0 if the payments are made at the end of the period, or 1 if payments are at the beginning.

For this example, the values are =-CUMIPMT(.04/12, 9, 10000, 1, 9, 0) = $167.41

Note that this amount of interest is far less than what would be owed if the loan were repaid in a single payment at the end of 9 months. In that case, interest would equal $10000 * .04/12 * 9, or $300.

With regular monthly payments, the principal amount outstanding declines each month, so less interest expense is incurred.

To illustrate this, you can build an amortization schedule using PMT, IPMT, and PPMT for each of the 9 periods. The PMT function yields a fixed monthly payment of $1,129.71. The IPMT function reveals that in the first period, $33.33 of the payment is interest and PPMT reveals that $1,096.38 is a repayment of the principal. That leaves a balance of $8,903.62 for the start of period 2. For the ninth and final payment of $1,129.71, only $3.75 is interest, and $1,125.96 repays the remaining balance.

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Answer 2

$10,000 * 4% * 9/12 = $300

Answer 3

10,000*.04=400

400*.75=300