Question

What is the future value of $100 after 3 years if the appropriate interest rate is 8%, compounded annually? ($125.97) Compounded monthly? ($127.02

Answer 1

The future value of $100 when compounded annually is $125.97 and when compounded monthly is $127.02.

Step-by-step explanation:

Compound interest is an interest rate calculation on the principal plus the accumulated interest. To calculate the future value of $100 after 3 years with an 8% interest rate, compounded annually, we use the formula:

`\[ \text{Future Value} = \text{Principal} * (1 + \text{Interest Rate})^{ \text{Time}} \]`

For annual compounding, the future value is obtained by applying the 8% interest rate for 3 years on the principal amount of $100:

Future Value =
`\$100 * (1 + 0.08)^3` = $125.97

For monthly compounding, we divide the interest rate by 12 and multiply the time by 12:

Future Value =
`\$100 * \left(1 + (0.08)/(12)\right)^(3 * 12)`= $127.02

Answer 2

Answer: If compounded annually, future value =$ 125.97

If compounded monthly, future value =$ 127.18

Step-by-step explanation:

Accumulated amount :
`A=P(1+(r)/(n))^(nt)`, where P=principal value, t= time, n= number of periods and r =rate of interest.

Given: Principal value = $100

Time = 3 years

rate of interest : r= 0.08

If compounded annually, n=1

`A=100(1+0.08)^3=100(1.08)^3=100*1.259712=\$125.97`

Hence, future value =$ 125.97

If compounded monthly, n=12

`A=100(1+(0.08)/(12))^(12*3)=100(1.0067)^(36)=100*1.271752=\$127.18`

Hence, future value =$ 127.18