Creating a retirement fund To supplement your planned retirement in exactly 42 years, you estimate that you need to accumulate 5220,000 by the end of 42 years from today. You plan to make equal, annual, end-of-year deposits into an account paying 8% annual interest. a. How large must the annual deposits be to create the $220,000 fund by the end of 42 years b. If you can afford to deposit only 5600 per year into the account, how much will yo have accumulated by the end of the forty-second year?
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a)To get the amount of each annual payment (PMT) ;
PMT={FVA _{42}} ÷(\frac{(1+0.08)^{42}-1} {0.08})PMT=FVA
42
÷(
0.08
(1+0.08)
42
−1
)
PMT=\frac{220,000}{304.244
PMT =$723.10
b)To calculate the future value, FVA;
FVA_{42}=PMT ×(\frac{(1+0.08)^{42}-1} {0.08})FVA
42
=PMT×(
0.08
(1+0.08)
42
−1
)
0.08})FVA
42
=PMT
Future value(FVA42) =$600× (304.244)
FVA=$182,546.40
Explanation:
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