Frodo made a down payment of $4,800 toward the purchase of a new ring. To pay the balance of the purchase price, he has secured a loan from Gimli at the rate of 7.2%/year compounded monthly. Under the terms of his finance agreement, he is required to make payments of $360/month for 42 months. What is the cash price of the ring?

Question

04-10-2021
Mathematics

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Frodo made a down payment of $4,800 toward the purchase of a new ring. To pay the balance of the purchase price, he has secured a loan from Gimli at the rate of 7.2%/year compounded monthly. Under the terms of his finance agreement, he is required to make payments of $360/month for 42 months. What is the cash price of the ring?

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francocanacari francocanacari · Answer 1 · 2021-10-13T12:36:29+02:00

The cash price of the ring was $ 16,560.80.

Knowing the down payment, the interest rate and the monthly payments, to determine what is the cash price of the ring, the following calculation must be performed, applying the compound interest formula:

Initial value x (1 + interest rate / compounding times) ^ (years x compounding times) = Compound interest
X x (1 + 0.072 / 12) ^ 3.5x12 = 360 x 42
X x 1.006 ^ 42 = 15,120
X x 1.2856 = 15,120
X = 15,120 / 1.2856
X = 11,760.80
11,760.80 + 4,800 = Cash price
16,560.80 = Cash price

Therefore, the cash price of the ring was $ 16,560.80.

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