If $5000 is invested at a rate of 3% interest compounded quarterly, what is the value of the investment in 5 years?
5000(1+.03/4)^(4*5) = 5805.92
5805.92 is the right answer
Well, well, well, if it isn't Mr. Moneybags! Let me put on my math hat and crunch some numbers for you. Hang on tight!
So, we've got $5000 being invested at an annual interest rate of 3%, compounded quarterly. In 5 years, huh? Alrighty then!
First, let's figure out the interest rate per quarter. Divide that 3% by 4, since there are 4 quarters in a year. That gives us a quarterly interest rate of 0.75%.
Next, multiply that quarterly interest rate by the number of quarters in 5 years. And voila! 20 quarters. So, 0.75% multiplied by 20 gives us a total interest rate of 15%.
Now, to calculate the value of the investment after 5 years, we add the interest to the initial investment. So, $5000 plus 15% of $5000 (which is $750) equals $5750.
Congratulations, my number-crunching friend! After 5 years, your investment will leap up to a whopping $5750. Ka-ching!
To find the value of the investment after 5 years with quarterly compounding, we can use the formula for compound interest:
A = P * (1 + r/n)^(nt)
Where:
A is the final amount
P is the principal amount (starting investment)
r is the annual interest rate (as a decimal)
n is the number of times the interest is compounded per year
t is the number of years
In this case, the principal amount (P) is $5000, the annual interest rate (r) is 3% expressed as 0.03, the number of times the interest is compounded per year (n) is 4 (quarterly compounding), and the number of years (t) is 5.
Using these values, we can calculate the value of the investment after 5 years:
A = 5000 * (1 + 0.03/4)^(4*5)
A = 5000 * (1.0075)^(20)
A ≈ 5000 * 1.157625
A ≈ $5788.13
Therefore, the value of the investment after 5 years with quarterly compounding at a 3% interest rate is approximately $5788.13.