Question

Yolanda invests $30,000 in an account that offers a compound interest rate of 7.9% per year. Which of the following is the correct equation for how much Yolanda will have in year 10?

Answer 1

The correct option will be Option D:      $P_{10} =30000(1+0.079)^{10$

The compounds interest can be estimated by using the following formula

$A =P(1+r/n)^{nt$

where

A: the final amount

P: the initial investment

r: the interest rate (in decimal)

n: the number of times the interest will be compounded per year

t: the time (in year)

Given in the problem that

the initial investment is $30,000 and the time period is 10 years,

so P=30000 and

t=10  

As we know The interest will be compounded one time per year

n=1.

now for converting the interest rate into decimal form, we will divide the rate of interest by 100.

r=7.9/100

⇒r=0.079

putting above values in the above formula

$A =P(1+r/n)^{nt$

⇒ $A =30000(1+0.079/1)^{(1)(10)$

⇒  $A =30000(1+0.079)^{10$

⇒$P_{10} =30000(1+0.079)^{10$

Therefore correct option is Option D:  $P_{10} =30000(1+0.079)^{10$

By completing the above equation to find the total amount

$P_{10} =30000(1+0.079)^{10$

⇒$P_{10} =30000(1.079)^{10$

⇒$P_{10} =64170.54$

Yolanda will have to pay $64,170.54 in her account after ten years.

Learn more about compound interest

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