As Jorge starts working now at the age of 22, he decides to make regular contributions to a savings account.He wants to accumulate enough by age 55 to fund an annuity of $4,800 per month until age 80.
What should his monthly contributions be? Assume that both accounts pay 8.5%, compounded
Monthly.Round to the nearest cent.
A)$274.82
B)$265.82
C)$261.08
D)$270.82
E)$288.82

Question

Quizplus · Accepted Answer

To calculate the monthly contributions required, we need to first calculate the total amount needed for the annuity payments.

The annuity payments will be made for 25 years (from age 55 to 80) and will be $4,800 per month. Therefore, the total amount needed will be:

$4,800 × 12 months × 25 years = $1,440,000

Now, we need to calculate how much Jorge needs to save each month to accumulate $1,440,000 by age 55, assuming an interest rate of 8.5% compounded monthly.

Using the annuity formula, we can calculate the present value of the annuity payments:

PV = annual payment ×[1 - (1 + r)^(-n)] / r

Where:
- PV is the present value of the annuity payments
- Annual payment is $4,800 × 12 months = $57,600
- r is the interest rate per period, which is 8.5% / 12 = 0.00708333
- n is the number of periods, which is (80 - 55) × 12 = 300

Plugging in the values, we get:

PV = $57,600 × [1 - (1 + 0.00708333)^(-300)] / 0.00708333
PV = $716,512.58

So, Jorge needs to accumulate $716,512.58 by age 55 in order to fund the annuity payments.

To calculate the monthly contributions required, we can use the present value formula:

PV = FV / (1 + r)^n

Where:
- FV is the future value we want to accumulate, which is $716,512.58
- r is the interest rate per period, which is 8.5% / 12 = 0.00708333
- n is the number of periods, which is (55 - 22) × 12 = 396

Plugging in the values, we get:

$716,512.58 = C / (1 + 0.00708333)^396

C = $716,512.58 × 0.00708333^396 / [1 - (1 + 0.00708333)^(-396)]
C = $274.82

Therefore, Jorge should contribute $274.82 per month to accumulate enough savings by age 55 to fund the annuity payments.

As Jorge Starts Working Now at the Age of 22