(Comprehensive problem) You would like to have $74,000 in 16 years. To accumulat
ID: 2809863 • Letter: #
Question
(Comprehensive problem) You would like to have $74,000 in 16 years. To accumulate this amount, you plan to deposit an equal sum in the bank each year that will eam 8 percent interest compounded annually. Your first payment will be made at the end of the yea 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 the lump-sum deposit be? (Assume you can eam 8 percent on this deposit.) c. At the end of year 5, you vill receive $20,000 and deposit it in the bank in an effort to reach your goal of $74,000 at the end of year 16. In addition to the lump-sum deposit, how much must you invest in 16 equal annual deposits to reach your goal? (Again, assume you can earn 8 percent on this deposit.) a. How much must you deposit annually to accumulate this amount? $ (Round to the nearest cent.)Explanation / Answer
a. To need $74,000 at the end of 16 years,
Interest rate = 8%
FVIF = P[(1+r)^n - 1)/r]
74000 = P[(1+0.08)^16 -1)/0.08]
= 74000 = P(30.3243)
P = $2,440.29
b. To make a lumpsum deposit:-
FV = P (1+r)^n
74000 = P (1+0.08)^16
74000 = P (3.4259)
P = $21,600
c. At the end of 5 year, we will receive $20000.
So, this lumpsum deposit at the end of 5th year, we will receive the below at the end of 16th year,
Amount = $20,000
Rate = 8%
N = 11 years
FV = P (1+r)^n
= 20,000 (1+0.08)^11
= $46,632.78
So, remaining value we require at the end of 16th year,
= 74,000 - 46,632.78
= $27,367.22
FVIF = P[(1+r)^n - 1)/r]
27367.22 = P[(1+0.08)^16 -1)/0.08]
= 27367.22 = P(30.3243)
P = $902.48
Yearly payment for 16 years = $902.48
Lumpsum at the end of 5th year = $20,000
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.