A newborn child receives a ​$5 comma 000 gift toward a college education from her grandparents. How much will the ​$5 comma 000 be worth in 17 years if it is invested at 4.9​% compounded​ quarterly?

Answer 1

The compound interest formula is A = P (1 + r/n)^nt, where P gives the initial, or principal amount invested, r is the annual interest rate, n is the number of compounding periods during the year, and t is the total number of years the money is invested for.

Assuming that, in your problem, 4.9% is an annual rate, we can use this formula like so: A = 5000(1 + 4.9%/4)^(4*17). We are using 4 for n because your question stipulates that there is quarterly compounding, so every 3 months the amount invested earns interest which is then added into the total investment amount. As another example, if you were using semi-annual compounding instead, you would use 2 instead of 4 for n. Solving the equation above, we get that the child will have 11,442.99 in 17 years if the 5000 has quarterly compounding interest.