Question

You want to receive ​$575 at the end of each year for 3 years. Interest is 6.1% compounded annually. ​

(a) How much would you have to deposit at the beginning of the 3​-year ​period? ​
(b) How much of what you receive will be​ interest?

Answer 1

To calculate the amount you would have to deposit at the beginning of the 3-year period, you can use the formula for the future value of an ordinary annuity. Substituting the given values into the formula, you would have to deposit approximately $1,630.76. The amount of what you receive that will be interest can be calculated by subtracting the total payment received from the total amount deposited.

Step-by-step explanation:

To calculate the amount you would have to deposit at the beginning of the 3-year period, we can use the formula for the future value of an ordinary annuity:

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

where FV is the future value, PMT is the periodic payment, r is the interest rate per period, and n is the number of periods.

For this problem, PMT = $575, r = 6.1% = 0.061, and n = 3.

Substituting these values into the formula, we get:

FV = ($575 * ((1 + 0.061)^3 - 1)) / 0.061

Solving this equation, we find that you would have to deposit approximately $1,630.76 at the beginning of the 3-year period.

To calculate the amount of what you receive that will be interest, we can subtract the total payment received from the total amount deposited: $1,630.76 - ($575 * 3) = $905.76.