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?

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.

[tex]A=P(1+\frac{r}{n})^{nt}[/tex], 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.

[tex]\frac{3.143}{100}=0.03143[/tex]

4 months will be equal to 1/3 year.

Substitute given values:

[tex]\$2021=P(1+\frac{0.03143}{12})^{12\times \frac{1}{3}}[/tex]

[tex]\$2021=P(1+0.0026191666666667)^{4}[/tex]

[tex]\$2021=P*1.0105178987881833656[/tex]

[tex]P*1.0105178987881833656=\$2021[/tex]

[tex]P=\frac{\$2021}{1.0105178987881833656}[/tex]

[tex]P=1999.96457[/tex]

[tex]P\approx \$2000[/tex]

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

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?

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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?