Small business?

Question

Need help. Mitch wants to borrow $12,000 to start a small business. He found a bank that offers a 5% discounted loan that is to be repaid in monthly installments over 10 years. How much should he borrow to get $12,000at the start of the loan?

Answer 1

I understand Jesus' confusion. Your question isn't worded well.

If Mitch wants to borrow $12,000...then he should borrow $12,000. That's the actual value of the loan at the time he borrows it.

What I think you want to know is, how much does he actually end up paying back to the bank?

If so then you'll need to use the loan formula:

P = Cr(1 + r)ⁿ/[(1 + r)ⁿ - 1]

to figure out how much his payment will be.

Again, I assume that by 5% you mean 5% per year compounded monthly, or 5%/12 = 0.41666667% per month.

10 years × (12 months/year) = 120 months of payments.

The payment would be:

P = Cr(1 + r)ⁿ/[(1 + r)ⁿ - 1]
P = $12,000(0.00417)(1 + 0.00417)^120/[(1 + 0.00417)^120 - 1]
P = $127.28 per month

So over 10 years, he would actually pay back:

120 months × ($127.28 per month) = $15,273.43

Is that the number you're looking for?

Answer 2

Well, if he needs 12,000. He should borrow the 12,000
If he borrows more, he will have to pay the bank more.