Nathan invested $3,500 in an account paying an interest rate of 3.5% compounded quarterly. Assuming no deposits or withdrawals are made, how much money, to the nearest hundred dollars, would be in the account after 19 years?
Answer
Attempt 1 out of 3
To solve this problem, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the final amount of money in the account
P = the initial amount of money (in this case, $3,500)
r = the interest rate (in decimal form, so 3.5% becomes 0.035)
n = the number of times interest is compounded per year (quarterly means 4 times per year)
t = the number of years (in this case, 19)
Plugging the values into the formula, we have:
A = 3500(1 + 0.035/4)^(4*19)
Simplifying:
A = 3500(1 + 0.00875)^(76)
A = 3500(1.00875)^(76)
Using a calculator, we find that (1.00875)^(76) is approximately 1.446.
Therefore,
A = 3500 * 1.446
A ≈ $5061
So, to the nearest hundred dollars, there would be approximately $5,100 in the account after 19 years.