Answer:
$3,193.50
Step-by-step explanation:
The general formula for final amount accrued is
[tex]\fbox{$A = P(1 + r/n)^{nt}$}[/tex]
where
- P = initial amount
- r = annual interest rate as a decimal (% interest/ 100)
- n = number of times compounded
- t = number of years
We are given
- A = 5000
- t = 15
- r = 3% = 3/100 = 0.03
- n = 4 since compounded quarterly and hence 4 times a year
Plugging in values we get
[tex]5000 = P(1 + 0.03/4)^{4*15}[/tex]
[tex]5000 = P(1 + 0.0075)^{60}\\\\5000 = P(1.0075)^{60}\\\\5000 = P * 1.565681\\[/tex]
Dividing both sides by 1.565681 gives us the value of P:
P = 5000/1.565681
P = $3,193.50
