Answer:
109.38
Explanation:
Recall the formula for compound interest is as follows:
A = P·(1 + r/n)nt , where
P = principal amount (initial amount deposited)
r = annual rate of interest (in decimal form)
t = # of years amount is deposited for
n = # of times interest is compounded per year
A = amount accumulated after t years, including interest
The problem asks how much money Heather will have in the bank by her 16th birthday when she deposited $100 on her 13th birthday in a bank with 3% interest compounded quarterly. From this, we have the following information:
P = $100
r = 0.03 ==> 3%/100% = 0.03
t = 3 years ==> 16 - 13 = 3
n = 4 ==> since there are 12 months per year and 12/4 = 3 months,
then interest is compounded every 3 months which is a total of 4 times per year
Therefore,
A = P(1 + r/n)nt
= 100(1 + 0.03/4)4·3
= 100(1 + 0.0075)12
= 100(1.0075)12
= 109.38069
≈ 109.38
Thus, Heather will have $109.38 in the bank by her 16th birthda