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 (11)/(100)\to &0.11\\ t=years\to (9)/(12)\to &(3)/(4) \end{cases} \\\\\\ 2700=P\left( 1+0.11\cdot (3)/(4) \right)`

solve for P

Answer 2

$ 2487.13 should be deposited. ( approx )

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 =
`(11)/(12)%` =
`(0.11)/(12)`

By substituting the values,

`2700 = P(1+(0.11)/(12))^9`

`\implies P = (2700)/((1+(0.11)/(12))^9)=2487.12544296\approx \$ 2487.13`