Tuition of
$1762
will be due when the spring term begins in
8
months. What amount should a student deposit today, at
5.47%,
to have enough to pay the tuition?
I assume you want this in simple interest.
let the amount needed now be A
A + A(.0547)(8/12) = 1762
A + A(.0364666..) = 1762
A(1.0364666..) = 1762
A = 1762/1.0364666.. = $1700.00
To find out the amount the student should deposit today, we need to calculate the future value of the deposit after 8 months at an interest rate of 5.47%.
The future value formula is given by:
Future Value = Present Value * (1 + Interest Rate)^(Number of Periods)
In this case, the future value we are looking for is $1762, the present value is what we need to calculate, the interest rate is 5.47%, and the number of periods is 8 months.
We can rearrange the formula to solve for the present value:
Present Value = Future Value / (1 + Interest Rate)^(Number of Periods)
Let's substitute the values into the formula and calculate:
Present Value = $1762 / (1 + 0.0547)^(8/12)
First, let's simplify the interest rate:
1 + 0.0547 = 1.0547
Next, calculate the exponent:
8/12 = 0.6667
Now let's substitute the values and calculate:
Present Value = $1762 / (1.0547)^(0.6667)
Using a calculator, evaluate (1.0547)^(0.6667) = 1.0349
Now, substitute the value back into the formula:
Present Value = $1762 / 1.0349
Solving for the present value:
Present Value ≈ $1,701.57
Therefore, the student should deposit approximately $1,701.57 today to have enough to pay the tuition of $1,762 when the spring term begins in 8 months at an interest rate of 5.47%.