Question

Lien Chen took out a single-payment loan for $2300.00 at 6.25% ordinary interest to pay for her federal income tax bill. If the loan’s maturity value is $2317.97, when would Lien have to pay back the loan if she took it out on April 1?

Answer 1

Using simple interest, it is found that she would have to pay the loan back on May 17.

Simple Interest

Simple interest is used when there is a single compounding per time period.

The amount of money after t years in is modeled by:

$A(t) = A(0)(1 + rt)$

In which:

• A(0) is the initial amount.

• r is the interest rate, as a decimal.

In this problem, the parameters are:

$A(t) = 2317.97, A(0) = 2300, r = 0.0625$

Solving for t, we have that:

$A(t) = A(0)(1 + rt)$

$2317.97 = 2300(1 + 0.0625t)$

$1 + 0.0625t = \frac{2317.97}{2300}$

$1 + 0.0625t + 1.00781304348$

$0.0625t = 0.00781304348$

$t = \frac{0.00781304348}{0.0625}$

$t = 0.125$

Considering a year has 365 days:

0.125 x 365 = 46

46 days after April 1, hence she would have to pay it back on May 17.

More can be learned about simple interest at https://brainly.com/question/25296782