Calculating Monthly Payments with Compound Interest
How can we determine the number of monthly payments Natasha has made on her loan?
What is the formula used to calculate the future value of an annuity with compound interest?
Finding the Number of Monthly Payments
Natasha takes out a loan with 12% annual interest compounded monthly. She makes monthly payments of $790, and after t monthly payments, she still owes $13,000.
For her t+1st monthly payment, $130 goes towards the interest. To find the number of monthly payments Natasha has made, we can use the formula for the future value of an annuity.
The formula to calculate the future value of an annuity with compound interest is FV = PMT * [(1+r)^n - 1] / r.
Where FV is the future value, PMT is the payment amount, r is the interest rate per period, and n is the number of periods.
By rearranging the formula and plugging in the given values, we can solve for t and find that Natasha has made approximately 54.89 monthly payments.
Natasha's loan has an interest rate of 12% per year compounded monthly. She makes monthly payments of $790, and after t monthly payments, she still owes $13,000. For her t+1st monthly payment, $130 goes toward the interest.
To find the value of t, we can use the formula for the future value of an annuity: FV = PMT * [(1+r)^n - 1] / r.
Using the given information and solving the equation, we find that t is approximately 54.89.