Final answer:
The cash price of the piano was approximately $4,566.63. The cost of financing was $617.37.
Step-by-step explanation:
To find the cash price of the piano, we need to calculate the present value of the loan payments.
The formula for calculating the present value of an annuity is:
PV = PMT * ((1 - (1 + r)^-n) / r)
Where PV is the present value, PMT is the monthly payment, r is the interest rate per period, and n is the number of periods.
In this case, the monthly payment is $108, the interest rate is 6.95% per period (0.0695/12), and the number of periods is 48 (4 years * 12 months).
Plugging in the values, we get:
PV = 108 * ((1 - (1 + 0.0695/12)^-48) / (0.0695/12))
This calculates to approximately $4,566.63. Therefore, the cash price of the piano was around $4,566.63.
To calculate the cost of financing, we subtract the cash price from the total amount paid over the loan term. The total amount paid is the monthly payment multiplied by the number of periods.
Total amount paid = 108 * 48 = $5,184
Cost of financing = Total amount paid - Cash price = 5,184 - 4,566.63 = $617.37