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% per year compounded quarterly over a period of 5 years. How much will the investment be
worth at the end of 5 years?
applying your standard formula, that would be
4.2M(1 + 0.054/4)^(4*5) = 5.49M
or more precisely,
$5,491,921.88
To find out how much the investment will be worth at the end of 5 years, you can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the final amount
P = the principal amount (in this case, $4.2 million)
r = annual interest rate (5.4%)
n = number of times interest is compounded per year (quarterly, so n = 4)
t = number of years (5)
Let's plug in the values into the formula and calculate the final amount:
A = 4,200,000(1 + 0.054/4)^(4*5)
First, calculate the interest rate per compounding period:
0.054/4 = 0.0135
Next, calculate the total number of compounding periods:
4 * 5 = 20
Now, substitute the values back into the formula and solve:
A = 4,200,000(1 + 0.0135)^(20)
A ≈ 4,200,000(1.0135)^(20)
A ≈ 4,200,000 * 1.2908
A ≈ 5,436,360
Therefore, the investment will be worth approximately $5,436,360 at the end of 5 years.
To find the worth of the investment at the end of 5 years, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = final amount
P = principal amount (initial investment)
r = annual interest rate (in decimal form)
n = number of times interest is compounded per year
t = number of years
In this case, the principal amount (P) is $4.2 million, the interest rate (r) is 5.4% (or 0.054 in decimal form), the interest is compounded quarterly (n = 4), and the investment period is 5 years (t = 5).
Plugging the values into the formula, we have:
A = 4.2 million * (1 + 0.054/4)^(4 * 5)
Calculating the values inside the parentheses first:
A = 4.2 million * (1 + 0.0135)^(20)
Using a calculator or spreadsheet, raise the value to the power of 20:
A ≈ 4.2 million * (1.0135)^(20)
A ≈ 4.2 million * (1.315173)
Calculating the final amount:
A ≈ $5,517,358.60
Therefore, at the end of 5 years, the investment will be worth approximately $5,517,358.60.