Question

Find the missing value in the compound amount formula. Attach complete solution and correct answer.

P=1000,
r=1%,
m=4,
n=16,
A=???
Rubric for scoring:

Answer 1

Using the compound interest formula with the given values of principal $1000, an annual interest rate of 1%, compounded quarterly, over 16 periods, the compound amount A is calculated to be $1,169.86.

Step-by-step explanation:

Compound Amount Calculation

To calculate the compound amount A, we can use the compound interest formula:

A = P(1 + r/m)^(mn)

We have the following given values:

Principal (P) = $1000

Annual interest rate (r) = 1% or 0.01 when expressed as a decimal

Number of times interest is compounded per year (m) = 4 (quarterly)

Total number of compounding periods (n) = 16

Substituting the provided information into the compound interest formula gives us:

A = 1000(1 + 0.01/4)^(4*16)

Calculate the values within the parentheses first:

A = 1000(1 + 0.0025)^(64)

A = 1000(1.0025)^(64)

Now, raising 1.0025 to the 64th power:

A = 1000*1.169858

Finally, multiply 1000 by 1.169858 to find the compound amount:

A = $1,169.86

Therefore, the compound amount A after 16 compounding periods is $1,169.86.