Answer :

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

  • A = final amount
  • 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