Question

Luisa borrowed to buy a piano, paying $123 at the end of each month for 3 years. The bank charges interest on the loan at 8.97% compounded monthly (a) What was the cash price of the piano? (b) How much is the cost of financing? (a) The cash price of the piano is $ (Round the final answer to the nearest cent as needed. Round all intermediate values to six decimal places as needed.) (b) The cost of financing is $ (Round the final answer to the nearest cent as needed. Round all intermediate values to six decimal places as needed.)

Answer 1

Solution -

(a) Calculation of Present Value Factor -

PV Factor = [1 - (1/(1+r)ⁿ)] / r

Where,

r = interest rate = 0.0897

n= number of periods =36 (3 Years*12)

i.e = [1 - (1/(1+0.0897)³⁶)] / 0.0897

= [1 - 1/22.031813]/0.0897

= [1 - 0.045389]/0.0897

= [0.954611]/0.0897

=10.64226

Calculation of Present Value -

Present Value = Future Value * PV Factor

Here,

Future Value is $123 & PV factor is 10.64226 (Calculated as above)

Hence,

Present Value = $123*10.64226

= $1309

The cash price of piano is $1309

(b) Calculation of cost of financing -

Total Cost of the Piano = $123*36 =$ 4428

Cash Price = $ 1309 (Calculated above)

Hence,

Financing Cost = Total cost - Cash Price

= $ 4428 - $1309

= $ 3119