Final answer:
To find out which financing option is cheaper for purchasing and shipping a statue, we need to calculate the monthly payments for each option using the formula for compound interest loans and then compare the total costs over the 4-year period.
Step-by-step explanation:
The question asks to determine the total cost of the cheaper option between financing a statue with the artist at a 20% interest rate, with shipping included, and financing through the bank at a 15.7% interest rate, with the need to pay for shipping separately.
To calculate the monthly payments and total cost of each option, we will use the formula for the monthly payment of a compound interest loan, which is
PV = R \[ \frac{1 - (1 + i)^{-n}}{i} \],
where PV is the present value (initial loan amount), R is the monthly payment, i is the monthly interest rate, and n is the total number of payments.
First, we calculate option A. If the artist finances the cost of the statue at 20% compounded monthly, we convert the annual rate to a monthly interest rate by dividing by 12: 20% / 12 = 1.6667%. The loan term is 4 years (or 48 months), so n is 48. We need to find the monthly payment R that satisfies PV = \$19750.
For option B, we do a similar calculation, but we also need to add the shipping cost of \$975 to the initial loan amount, since this option does not include free shipping. The bank's interest rate is 15.7%, so the monthly rate is
15.7% / 12 = 1.3083%.
We will use the same formula to find the monthly payment R for the increased initial loan amount of
PV = \$19750 + \$975 and the same loan term of 4 years (48 months).
After calculating R for both options, we multiply the monthly payment by 48 to get the total cost of each loan. The option with the lower total cost is the cheaper one.