Question

How much would $14,250 be worth in a savings account after 13 years if the account has a 5.25% APY and the interest is compounded weekly?
Use the compound interest formula to find the account balance after 13 years.

Answer 1

Answer:

$28,188.46

Step-by-step explanation:

The formula you need is:

$A(t)=P(1+\frac{r}{n})^{nt}$

Where A(t) is the amount after the compounding, P is the initial investment, r is the interest rate, n is the number of compoundings per year, and t is the time in years.  We are looking for A(t).  P is $14,250; r in decimal form is .0525; n is 52 since there are 52 weeks in a year; t is 13 years.  Filling in:

$A(t)=14,250(1+\frac{.0525}{52})^{(52)(13)}$

Simplifying inside the parenthesis and the exponential multiplication:

$A(t)=14,250(1.0010096154)^{676}$

Raising the number in parenthesis to the power of 676 gives us:

A(t) = 14,250(1.978137432)

Multiplying then gives us $28,188.46