Question
4. In 8 years, the investment Helen made at 8% compounded quarterly,will have grown to 25000 a) What was her initial investment?
Solution
4.3
(299 Votes)
Aldric
Professional ยท Tutor for 6 years
Answer
### $13386.66
Explanation
## Step 1: Define Variables and Formula### We are given the future value (
), interest rate (
), compounding periods per year (
), and time (
). We need to find the principal (
). The formula for compound interest is
.## Step 2: Plug in Values###
25000
r = 8\% = 0.08
n = 4
t = 8
25000 = P(1 + \frac{0.08}{4})^{4 \cdot 8}
25000 = P(1 + 0.02)^{32}
25000 = P(1.02)^{32}
(1.02)^{32} \approx 1.8674
25000 = P \cdot 1.8674
1.8674
P
P = \frac{25000}{1.8674} \approx 13386.66$.