Question

Consider the following future value. (Round your answers to the nearest cent.)

$4,412 at 10 and 3/4 % compounded quarterly for 6 years

(a) Find the present value that will generate the given future value.
$ ...

(b) Interpret the present value.

One would have to invest $ ... now to have the future value in the given time.

Answer 1

FV = PV (1 + r)ⁿ

=> PV = FV / (1+r)ⁿ

where, FV = Future Value = $ 4412 (given)

PV = Present Value, i.e amount to be invested today (in the given context)

r = interest rate per compounding period.

As the compounding is done quarterly, for 6 years, r = 10.75% / 4 = 2.6875%

n = Number of Compounding periods = 6 Years compounded quarterly = 6 years x 4 quarters per year = 24. Thus, n = 24

So,

PV = 4412 / [(1+2.6875%)²⁴] = 4412 / [(1.026875)²⁴] = $ 2334.61

One would have to invest $ 2,334.61 now to have the future value $ 4,412 in the 6 years at 10.75% interest rate, compounded quarterly

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