Nick would like to purchase a vacation timeshare, but he can only afford a $350 monthly loan payment. He wants the loan to extend 20 years, and the annual interest rate is 6%. How much money will Nick need to borrow if he repays the loan at $350 per month over the 20-year period of the loan?
350=P * (0.06*20)/12
That's a very creative formula you have there, but it makes no sense to me.
You want the present value of monthly payments of $350 for 20 years at 6% compounded monthly
PV = 350(1 - 1.005^-240)/.005
= 48,853.27
Btw, your P value turns out to be 319.50
Did you find that formula in your text or your notes ?
This question was in a math competition on April 2nd. I could The answer given was 48853.00
why a negative -240?
That's the way the standard formula is.
notice I had the correct answer.
To find out how much money Nick will need to borrow, we can rearrange the loan repayment formula. The formula is:
Loan amount = Monthly payment / ((Annual interest rate/12) * Term in months)
Now, let's substitute the given values into the formula:
Monthly payment = $350
Annual interest rate = 6%
Term = 20 years
First, let's convert the annual interest rate to a monthly interest rate. We divide it by 12:
Monthly interest rate = 6% / 12 = 0.005
Next, we need to calculate the number of months in 20 years:
Term in months = 20 years * 12 months/year = 240 months
Now, we can substitute the values into the loan repayment formula:
Loan amount = $350 / ((0.005) * 240)
Simplifying the equation:
Loan amount = $350 / (0.012)
Loan amount = $29,166.67
Therefore, Nick will need to borrow approximately $29,166.67 in order to repay the loan at $350 per month over the 20-year period.