Question

What lump sum deposited today at 8 ?% compounded quarterly for 15 years will yield the...

What lump sum deposited today at 8 ?% compounded quarterly for 15 years will yield the same final amount as deposits of ?$6000 at the end of each? 6-month period for 15 years at 8 ?% compounded? semiannually?

The value of the lump sum is?

Homework Answers

Answer #1
$ 1,02,562.17

Working:

a. Calculate future value of 6-month deposits
Future Value = 6-month deposits x future Value of 6-month deposits for 15 years
= $       6,000.00 x 56.08494
= $ 3,36,509.63
Working:
Future Value of 6-month deposits for 15 years = (((1+i)^n)-1)/i Where,
= (((1+0.04)^30)-1)/0.04 i 4%
= 56.08494 n 30
b. Present Value of amount to be deposited
Present Value = F*(1+i)^-n Where,
= 336509.63*(1+0.02)^-60 i 8%/4 = 0.02
= $ 1,02,562.17 n 15*4 = 60
F = $ 3,36,509.63
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