The manager of a money market fund has invested $4.2 million in certificates of deposit that pay interest at the rate of 5.4%/year compounded quarterly over a period of 5 years. How much will the investment be worth at the end of 5 years?
in millions,
4.2(1+.054/4)^(4*5)
$5.491921.88
To calculate the future value of the investment, we can use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A = future value of the investment
P = principal amount (initial investment)
r = annual interest rate (in decimal form)
n = number of compounding periods per year
t = number of years
In this case, the principal amount (P) is $4.2 million, the annual interest rate (r) is 5.4% (or 0.054), the number of compounding periods per year (n) is 4 (quarterly compounding), and the number of years (t) is 5.
Plugging in the values into the formula:
A = 4.2 million * (1 + 0.054/4)^(4 * 5)
Step by step calculation (∵ BODMAS rule):
1. Divide the annual interest rate by the number of compounding periods per year: 0.054/4 = 0.0135
2. Add 1 to the result: 1 + 0.0135 = 1.0135
3. Raise the result to the power of the total number of compounding periods: (1.0135)^(4 * 5) = (1.0135)^20
Now, let's calculate the final value (A):
A = 4.2 million * (1.0135)^20
Using a calculator, we can find:
A ≈ 4.2 million * 1.318382662 ≈ 5,530,617.65
Therefore, the investment will be worth approximately $5,530,617.65 at the end of 5 years.