Question

(Comprehensive problem) You would like to have $58, this amount, you plan to deposit an equal sum in the bank each year that will earn 9 percent interest compounded annually. Your first payment will be made at the end of the year. a. How much must you deposit annually to accumulate this amount? b. If you decide to make a large lump-sum deposit today instead of the annual deposits. how large should this lump-sum deposit be? (Assume you can earn 9 percent on c. At the end of five years, you will receive $20,000 and deposit this in the bank toward this deposit.) your goal of $58,000 at the end of year 15. In addition to the lump-sum deposit, how much must you deposit in equal annual amounts, beginning in year 1 to reach your goal? (Again, assume you can earn 9 percent on your deposits.) a. How much must you deposit annually to accumulate this amount? (Round to the nearest cent.)

Answer 1

To accumulate $58,000 at the end of year 15, you must deposit approximately $3,101.04 annually. The lump-sum deposit you need to make today to reach your goal is approximately $19,051.40.

Step-by-step explanation:

To determine the amount you need to deposit annually in order to accumulate $58,000 at the end of year 15, you can use the formula for the future value of an annuity:

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, and n is the number of periods.

Using the given information, we have:

FV = $58,000
r = 0.09
n = 15

Substituting the values into the formula:

$58,000 = P * [(1 + 0.09)^15 - 1] / 0.09

Solving for P, we find that you must deposit approximately $3,101.04 annually to accumulate $58,000 at the end of year 15.

To determine the lump-sum deposit you need to make today in order to reach your goal of $58,000 at the end of year 15, you can use the formula for the present value of a lump-sum:

PV = FV / (1 + r)^n

Using the given information, we have:

PV = $58,000
r = 0.09
n = 15

Substituting the values into the formula:

$58,000 = PV / (1 + 0.09)^15

Solving for PV, we find that the lump-sum deposit you need to make today is approximately $19,051.40.