Question

Luca found an ordinary annuity that earns 3.3%. He will deposit $270.00 each month into his account for the next 28 years. How much interest, in total, will he earn? How much will his account be worth at the end of the 28 years? How much of the ending account balance comes from deposits?

Answer 1

Answer: Amount from Deposits = FV - Interest = $177,057.14 - $86,337.14 = $90,720.

Explanation:

To find the total interest earned, we need to first find the total amount of money that Luca will deposit over 28 years. We can use the formula for the future value of an annuity to find this amount:

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

where PMT is the monthly payment, r is the monthly interest rate, and n is the number of months.

Plugging in the values, we get:

FV = 270 x (((1 + 0.033/12)^(28*12) - 1) / (0.033/12)) = $177,057.14

So, Luca will deposit a total of $270 x 12 months/year x 28 years = $90,720.

The interest earned will be the difference between the total amount in the account at the end of 28 years and the total amount of deposits:

Interest = FV - Total Deposits = $177,057.14 - $90,720 = $86,337.14

The account will be worth $177,057.14 at the end of 28 years.

The amount of the ending account balance that comes from deposits is the difference between the ending account balance and the interest earned:

Amount from Deposits = FV - Interest = $177,057.14 - $86,337.14 = $90,720.