Question

Tuition of $2700 is due when the spring term begins, in 9 months. What amount should a student deposit today at 11%, to have enough to pay tuition?

Answer 1

bearing in mind "t" in the simple interest equation, is for years, and 9months is just 9 off 12 months in a year

then  $\bf \qquad \textit{Simple Interest Earned Amount}\\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\to &\ 2700\\ P=\textit{original amount deposited}\\ r=rate\to 11\%\to \frac{11}{100}\to &0.11\\ t=years\to \frac{9}{12}\to &\frac{3}{4} \end{cases} \\\\\\ 2700=P\left( 1+0.11\cdot \frac{3}{4} \right)$

solve for P

Answer 2

Answer:

$ 2487.13 should be deposited. ( approx )

Step-by-step explanation:

Since, future value formula,

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

Where,

P = Principal amount,

r = rate per periods

n = number of periods,

Given,

A = $ 2,700,

t = 9 months,

Annual rate = 11%,

So, the monthly rate, r = $\frac{11}{12}%$ = $\frac{0.11}{12}$

By substituting the values,

$2700 = P(1+\frac{0.11}{12})^9$

$\implies P = \frac{2700}{(1+\frac{0.11}{12})^9}=2487.12544296\approx \ 2487.13$