Alicia invested $32000 into an account earning 3% annual interest compounded quarterly. She makes no other deposits and does not withdraw any money. What is the balance of Alicia's account in 7 years?
The formula for compound growth is:
\(P=P_{0}(1+\frac{r}{n})^{nt}\)
Where,
We need to solve for P. From the given information, we can write:
\(P_{0}=32,000\)
\(r=\frac{3}{100}=0.03\)
\(n=4\) (since compounded quarterly)
\(t=7\)
Plugging in all the information in the equation, we get:
\(P=32,000(1+\frac{0.03}{4})^{(4)(7)} \\P=32,000(1.0075)^{28}\\P=32,000(1.2327)\\P=39,446.4\)
Alicia's account balance at end of 7 years is $39,446.4.
ANSWER: $39,446 (rounded to the nearest dollar)
The interest earned on the amount will increase the net balance. Thus, the balance of Alicia's account in 7 years would become $39,446.78 approximately.
If the initial amount (also called as principal amount) is P, and the interest rate is R% per unit time, and it is left for T unit of time for that simple interest, then the interest amount earned is given by:
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And thus, final amount will be:
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For the given case, the principal amount (initial amount) Lynne invested is P = 32000 (in dollars)
The rate of interest = 3% annual interest compounding quarterly.
or 3%/4 = 0.75% quarterly interest compounding quarterly. = R
Here, unit of time is is quarter of an year which means 1/4 of an year.
The time is given to be 7 years. In each year, there are 4 quarters, so in 7 years, there would be @@MATH_TOKEN_2@@ quarters of years.
Thus, T = 28 (we always need to keep unit of time same for R and T for using that formula).
Putting these values in the above formula, we get the final amount's value in Alicia's account in 28 years as:
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Thus, the balance of Alicia's account in 7 years would become $39,446.78 approximately.
Learn more about compound interest here:
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