Question

To find the cash price of the piano, we can work backward from the monthly payments that Luisa is making and use the formula for the present value of an annuity.

The monthly payments Luisa is making are $129, and the loan term is 5 years, which means she will make 5 * 12 = 60 monthly payments.
The interest rate is 6.47% compounded monthly, so we need to find the monthly interest rate as a decimal, which is 6.47\% / 12 = 0.5392\%6.47%/12=0.5392% or 0.005392 as a decimal.

Answer 1

To find the cash price of the piano, Luisa needs to make 60 monthly payments of $129 at a 6.47% monthly interest rate.

Step-by-step explanation:

Luisa's monthly payments of $129 for 5 years constitute an annuity. To determine the cash price, we use the present value of an annuity formula. The loan term of 5 years results in 60 monthly payments (5 * 12). The interest rate, compounded monthly at 6.47%, is converted to a decimal (0.5392%). With these values, the formula helps unravel the present value, representing the cash price.

This method allows Luisa to understand the current value of her future payments, providing insight into the total cost of the piano. It's a fundamental financial calculation, especially in scenarios where individuals make regular payments towards a larger sum. In this case, the monthly payment, loan term, and interest rate play crucial roles in determining the initial cash value.

Understanding present value in financial calculations helps individuals make informed decisions about loans and investments. It forms the basis for assessing the true cost of an obligation or the value of an investment over time.