You deposit $6,700 in a money-market account that pays an annual interest rate of 3.3%. The interest is compounded quarterly. How much money will you have after 4 years?
how many quarter years in 4 years
4*4 = 16 quarters
quarterly interest rate = .033/4 = .00825
so every quarter we multiply what we have by 1.00825
16 times we do that so
1.00825^16 = 1.140490549
now multiply that by the starting amount 6700
= $7,641.29
To calculate the amount of money you will have after 4 years, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the final amount of money
P = the principal amount (initial deposit) = $6,700
r = annual interest rate (in decimal form) = 3.3% = 0.033
n = number of times interest is compounded per year = 4 (quarterly)
t = number of years
Substituting these values into the formula, we get:
A = 6700(1 + 0.033/4)^(4*4)
A = 6700(1.00825)^(16)
Now, we need to calculate (1.00825)^16:
(1.00825)^16 ≈ 1.059837
Substituting this back into the equation:
A = 6700 * 1.059837
A ≈ $7,112.29
Therefore, after 4 years, you will have approximately $7,112.29 in the money-market account.