Knowing that the education costs for her kids would be huge, Roberta puts lump sum money from her inheritance in a savings account paying an interest of 4.69% compounded semi-annually. If ordinary annuity payments of $1500.00 per month are to be paid out of the account at the end of each month for four years, how much did Roberta deposit?

Question

Quizplus · Accepted Answer

Using the formula for the future value of an ordinary annuity:

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

where PMT is the monthly payment, i is the interest rate per compounding period (semi-annually in this case), and n is the number of compounding periods (8 in this case, since there are 4 years and payments are made monthly).

Solving for FV, we get:

FV = $1500 x ((1+0.0469/2)^8 - 1) / (0.0469/2) = $79,128.12

To find the present value (PV) of this annuity, we need to discount the future value by the same semi-annual interest rate used for compounding:

PV = FV / (1 + i/2)^n

PV = $79,128.12 / (1 + 0.0469/2)^8 = $65,592.15

Therefore, Roberta deposited $65,592.15 in the savings account.

Knowing That the Education Costs for Her Kids Would Be