angela deposits $1000 into an account with an apr of 2.9% for 11 years. find the future value of the account…

angela deposits $1000 into an account with an apr of 2.9% for 11 years. find the future value of the account if interest is compounded weekly. round your answer to two decimal places. formulas simple interest i = prt future value for simple interest a = p(1 + rt) future value for compound interest a = p(1 + r/n)^nt future value for continuous compound interest a = pe^rt annual percentage yield (apy) apy = (1 + r/n)^n - 1 answer

angela deposits $1000 into an account with an apr of 2.9% for 11 years. find the future value of the account if interest is compounded weekly. round your answer to two decimal places. formulas simple interest i = prt future value for simple interest a = p(1 + rt) future value for compound interest a = p(1 + r/n)^nt future value for continuous compound interest a = pe^rt annual percentage yield (apy) apy = (1 + r/n)^n - 1 answer

Answer

Explanation:

Step1: Identify the values

$P = 1000$ (principal amount), $r=0.029$ (annual - interest rate, since $2.9%=0.029$), $n = 52$ (number of compounding periods per year as compounded weekly), $t = 11$ (number of years).

Step2: Use the compound - interest formula

The compound - interest formula is $A=P(1 +\frac{r}{n})^{nt}$. Substitute the values: $nt=52\times11 = 572$, $\frac{r}{n}=\frac{0.029}{52}\approx0.0005577$. Then $1+\frac{r}{n}=1 + 0.0005577=1.0005577$. $(1+\frac{r}{n})^{nt}=(1.0005577)^{572}$. Using a calculator, $(1.0005577)^{572}\approx1.3777$. $A = 1000\times(1.0005577)^{572}\approx1000\times1.3777 = 1377.74$.

Answer:

$1377.74$