Question

Doris purchased a piano with​ $300 down and​ end-of-month payments of​ $124 for​ two-and-a-half years at​ 9% compounded monthly. What was the purchase price of the​ piano? Question content area bottom Part 1 The purchase price of the piano was ​$ enter your response here. ​(Round the final answer to the nearest cent as needed. Round all intermediate values to six decimal places as​ needed.)

Answer 1

The purchase price of the​ piano is $3620.05866.

To determine the purchase price of the piano, we can use the present value formula for an annuity. The formula is given by:

`P=PMT*( 1-(1+r)^-^n^t/r)+D`

Here,

PMT represents the monthly payment, which is $124,r is the monthly interest rate expressed as a decimal, calculated as 9%/12=0.0075

n is the total number of payments, given by 2.5×12,D denotes the down payment, which is $300.

Plugging these values into the formula, we get:

`P=124*( 1-(1+0.0075)^-^(^2^.^5^*^1^2^)/0.0075 )+300`

After performing the calculations, the result is approximately $3620.05866. Therefore, the purchase price of the piano is approximately $3620.06 when rounded to the nearest cent.