Question

Tuition of ​$2021 will be due when the spring term begins in 4 months. What amount should a student deposit​ today, at 3.143%, to have enough to pay the​ tuition?

Answer 1

$2000

Explanation:

We have been given that tuition of ​$2021 will be due when the spring term begins in 4 months. We are asked to find the amount that a student should deposit​ today, at 3.143%, to have enough to pay the​ tuition.

We will use compound interest formula to solve our given formula.

`A=P(1+(r)/(n))^(nt)`, where,

A = Final amount,

P = Principal amount,

r = Annual interest rate in decimal form,

n = Number of times interest is compounded per year.

t = Time in years.

Let us convert given interest rate in decimal form.

`(3.143)/(100)=0.03143`

4 months will be equal to 1/3 year.

Substitute given values:

`\$2021=P(1+(0.03143)/(12))^{12* (1)/(3)}`

`\$2021=P(1+0.0026191666666667)^(4)`

`\$2021=P*1.0105178987881833656`

`P*1.0105178987881833656=\$2021`

`P=(\$2021)/(1.0105178987881833656)`

`P=1999.96457`

`P\approx \$2000`

Therefore, the student should deposit $2000 today to have enough to pay the​ tuition.