Question

Find the future value and interest earned if $8806.54 is invested for 7 years at 6% compounded

Answer 1

(a)

The formula for future value of an amount of money is given by >>>

`FV=PV(1+r)^t`

Where

FV is the future value

PV is the present value

r is the rate of interest per period, in decimal

t is the time period

Given,

PV = 8806.54

Rate of interest is 6% annual, so semi annual compounding means that r = 6%/2 = 3% = 0.03

In 7 years, there are 7 x 2 = 14 compoundings, since semi annual compounding. We use t = 14

Plugging all the information, we get:

`\begin{gathered} FV=PV(1+r)^t \\ FV=8806.54(1+0.03)^(14) \\ FV=8806.54(1.03)^(14) \\ FV=13,320.68 \end{gathered}`

The future value at semi-annual compounding is $13,320.68

The interest earned is about $13,320.68 - $8806.54 = $4514.14

(b)

When we are continuously compounding, we use a slightly different formula. That is

`A=Pe^(rt)`

Where

A is the future value

P is the initial amount

r is the rate of interest

t is the time period

We know,

P = 8806.54

r = 6% = 0.06

t = 7

So, plugging in gives us,

`\begin{gathered} A=Pe^(rt) \\ A=(8806.54)e^(0.06*7) \\ A=(8806.54)e^(0.42) \\ A=13,403.22 \end{gathered}`

The future value at continuous compounding is $13,403.22

The interest earned is about $13,403.22 - $8806.54 = $4596.68