Question

Mike buys a ring for his fiancee by paying $30 a month for one year. If the interest rate is 10% per year, compounded monthly, what is the price of the ring?

Answer 1

To find the price of the ring, we need to calculate the present value of the monthly payments made by Mike over one year.

The formula to calculate the present value of a series of equal payments is:

PV = PMT * (1 - (1 + r)^(-n)) / r

Where:
PV is the present value (price of the ring),
PMT is the monthly payment ($30),
r is the interest rate per period (10% per year, compounded monthly),
n is the number of periods (12 months).

Substituting the values into the formula:

PV = 30 * (1 - (1 + 0.10/12)^(-12)) / (0.10/12)

Calculating the expression inside the parentheses:

PV = 30 * (1 - (1.008333)^(-12)) / (0.008333)

Using a calculator to evaluate the expression:

PV ≈ 30 * (1 - 0.9037) / 0.008333
PV ≈ 30 * 0.0963 / 0.008333
PV ≈ 289.00

Therefore, the price of the ring is approximately $289.00.

Answer 2

To find the price of the ring, we can use the formula for the future value of an annuity. The price of the ring is approximately $358.50.

Step-by-step explanation:

To find the price of the ring, we can use the formula for the future value of an annuity.

The future value of an annuity formula is:

FV = P * ((1 + r)^n - 1) / r

Where:

• FV is the future value
• P is the periodic payment
• r is the interest rate per period
• n is the number of periods

In this case, the periodic payment is $30, the interest rate is 10% per year, compounded monthly, and the number of periods is 12 (since the payments are made monthly for one year).

Plugging these values into the formula, we get:

FV = 30 * ((1 + 0.1/12)^12 - 1) / (0.1/12)

Simplifying this expression, we find that the future value of the annuity is approximately $358.50.

Therefore, the price of the ring is approximately $358.50.