william puts $7,000.00 into an account to use for school expenses. the account earns 12% interest…

william puts $7,000.00 into an account to use for school expenses. the account earns 12% interest, compounded monthly. how much will be in the account after 5 years? use the formula a = p(1 + r/n)^nt, where a is the balance (final amount), p is the principal (starting amount), r is the interest rate expressed as a decimal, n is the number of times per year that the interest is compounded, and t is the time in years. round your answer to the nearest cent.

william puts $7,000.00 into an account to use for school expenses. the account earns 12% interest, compounded monthly. how much will be in the account after 5 years? use the formula a = p(1 + r/n)^nt, where a is the balance (final amount), p is the principal (starting amount), r is the interest rate expressed as a decimal, n is the number of times per year that the interest is compounded, and t is the time in years. round your answer to the nearest cent.

Answer

Explanation:

Step1: Identify values

$P = 7000$, $r=0.12$, $n = 12$, $t = 5$

Step2: Substitute into formula

$A=7000\left(1+\frac{0.12}{12}\right)^{12\times5}$

Step3: Calculate inside - parentheses first

$1+\frac{0.12}{12}=1 + 0.01=1.01$

Step4: Calculate exponent

$12\times5 = 60$, so we have $A = 7000\times(1.01)^{60}$

Step5: Calculate $(1.01)^{60}$

Using a calculator, $(1.01)^{60}\approx1.816696698$

Step6: Calculate $A$

$A=7000\times1.816696698\approx12716.88$

Answer:

$$12716.88$