Question

Find the future value. (Use the Table 12.1.) (Do not round intermediate calculations. Round the "FV factor" to 4 decimal places and final answer to the nearest cent.)

Present value: $7,692.96

Length of time: 7 times

Rate: 12%

Compounded: Quarterly

Period used: 28

Rate used: 3%

FV factor used: ______________ ?

Future value_________________ ?

Answer 1

The future value (FV) of an investment of present value (PV) dollars earning interest at an annual rate of r compounded m times per year for a period of t years is:

$FV=PV(1+r/m)^{mt}$

or

$FV=PV(1+i)^{n}$

where i = r/m is the interest per compounding period and n = mt is the number of compounding periods.

We have:

$i=12/4=3\ \%$ , $n=7$

Then:

FV factor used:

$(1+i)^n=1.03^7=1.2299$

Future value:

$FV=7692.96\cdot1.2299=\$\ 9461.37$