nadine -- Please use the Post a New Question link to ask your questions. Don't piggyback on another student's question.
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nadine's question --
Karen deposited $4000 into an account with 2.4% interest, compounded quarterly. Assuming that no withdrawals are made, how much will she have in the account after 9 years?
just plug it into the usual formula:
4000(1 + 0.024/4)^(4*9) = ?
2.4/ 4 = 0.60% per quarter = 0.0064
9 years = 36 quarters
so
4000 (1.0064)^36
=4000 * 1.25818
To calculate the amount Karen will have in the account after 9 years with compound interest, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A is the final amount (amount Karen will have after 9 years)
P is the principal amount (initial deposit) which is $4000
r is the annual interest rate as a decimal, which is 2.4% or 0.024
n is the number of times the interest is compounded per year, which is quarterly or 4 times
t is the number of years, which is 9
Using the formula, we substitute the values:
A = 4000(1 + 0.024/4)^(4*9)
To calculate this, we solve the expression in parentheses first:
(1 + 0.024/4) = 1.006
Now we substitute this value back into the formula:
A = 4000 * 1.006^(4*9)
Calculating the exponent:
A = 4000 * 1.6034
A ≈ $6413.60
Therefore, Karen will have approximately $6413.60 in the account after 9 years, assuming no withdrawals are made.