Question

What lump sum deposited today at 12​% compounded quarterly for 10 years will yield the same final amount as deposits of ​$3000 at the end of each​ 6-month period for 10 years at ​10% compounded​ semiannually?

The value of the lump sum is $___

Answer 1

- A lumpsum amount deposit today for 10 years will have the same future value as the Semi-annual periodic deposit for 10 years.

Calculating the Future Value of Semi-annual periodic deposit using FV annuity formula:-

Where, C= Periodic Payments = $3000

r = Periodic Interest rate = 10%/2 = 5%

n= no of periods = 10 years*2 = 20

Future Value = $99,197.86

Now, the Lumpsum deposit will have the same Future Value.

Calculating the Present Value of amount of lumpsum deposit:-

r = Periodic Interest rate = 12%/4 = 3%

n= no of periods = 10 years*4 = 40

Present value = $30,409.78

So, lump sum deposited today is $30,409.78

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