Question

To pay for a new machinery and tool years and companies owner invest $20,000 at 5.5% compounded quarterly how much money will be available in 10 years round your answer to the nearest cent

Answer 1

Given:

Principal (Investment) = $20,000

Interest Rate = 5.5% or 0.055 in decimal form

Time = 10 years

Compounding period = quarterly = 4 in every year

Find: the accrued amount or final amount after 10 years with interest

Solution:

To find the final amount after 10 years, we use the formula below.

`F=P(1+(r)/(m))^(mt)`

where:

P = principal = $20,000

r = interest rate = 0.055

m = compounding period = 4

t = time = 10 years

Let's plug into the formula the values of each variable.

`F=20,000(1+(0.055)/(4))^(4*10)`

Solve for F.

a. Add the terms inside the parenthesis and multiply the exponents outside.

`F=20,000(1.01375)^(40)`

b. Apply the exponent.

`F=20,000(1.726770771)`

c. Multiply the two numbers.

`\begin{gathered} F=34,535.41542 \\ F\approx34,535.42 \end{gathered}`

Answer:

After 10 years, there will be $34,535.42 available.