Question

Points: 0 of 1Find the future value and interest eamed if $8904.56 is invested for 7 years at 4% compounded (a) semiannually and (b) continuously(a) The future value when interest is compounded semiannually is approximately $(Type an integer or decimal rounded to the nearest hundredth as needed.)

Answer 1

a) Future value = $11,749.38

Interest = $2,844.82

b) Future value = $11,717.79

Interest = $2,813.23

Explanations:

The formula for calculating the future amount (compound amount) is expressed as;

`\begin{gathered} A=P(1+(r)/(n))^(nt) \\ \end{gathered}`

P is the amount invested

r is the rate (in decimal)

n is the compounding time

t is the time (in years)

Given the following parameters:

`\begin{gathered} P=$\$8904.56$ \\ t=7\text{years} \\ n=2(semi-annually) \\ r=4\%=0.04 \end{gathered}`

Substitute the given parameters into the formula:

`\begin{gathered} A=8904.56(1+(0.04)/(2))^(2(7)) \\ A=8904.56(1+0.02)^(14) \\ A=8904.56(1.02)^(14) \\ A=8904.56(1.3195) \\ A\approx\$11,749.38 \end{gathered}`

Hence the future value if the amount invested is compounded semiannually is approximately $11,749.38

Calculate the interest;

`\begin{gathered} A=P+I \\ I=A-P \\ I=\$11,749.38-\$8904.56 \\ I=\$2,844.82 \end{gathered}`

b) If the amount invested is compounded continuously, this means that

n = 1. Using the previous formula and replacing the value of "n" as 1 will give;

`\begin{gathered} A=P(1+(r)/(n))^(nt) \\ A=8904.56(1+(0.04)/(1))^(1(7)) \\ A=8904.56(1.04)^7 \\ A=8904.56(1.3159) \\ A=\$11,717.79 \end{gathered}`

The future value when interest is compounded continuously is approximately $11,717.79

Get the interest if compounded continuously

`\begin{gathered} A=P+I \\ I=A-P \\ I=11,717.79-8904.56 \\ I\approx\$2,813.23 \end{gathered}`

Hence the interest on the amount invested if compounded continuously is $2,813.23