Question

A bank features a savings account that has an annual percentage rate of r = 3.6% with interest compoundedquarterly. Haley deposits $10,000 into the account.The account balance can be modeled by the exponential formula Ale) = a(1+)*,, where A is accountvalue after t years, a is the principal (starting amount), r is the annual percentage rate, k is the number oftimes each year that the interest is compounded.(A) What values should be used for a, r, and k?a =10000T0.036 ok=4(B) How much money will Haley have in the account in 9 years?Answer = $ 13800Round answer to the nearest penny.(C) What is the annual percentage yield (APY) for the savings account? (The APY is the actual or effectiveannual percentage rate which includes all compounding in the year).APY =Round answer to 3 decimal places.

Answer 1

The answer to the part C:

Part C asking for APY ( Annual percentage yield )

APY is giving by the formula:

$\text{APY}=(1+\frac{r}{k})^k-1$

Where: r is the annual percentage rate.

k is the number of times each year that the interest is compounded.

Given: r = 3.6% = 0.036 , k = 4

Substitute with (r) and (k) into the formula of APY

So,

$\text{APY}=(1+\frac{0.036}{4})^4-1=1.0364889-1=0.0364889=3.64889\%$

Rounding to 3 decimal places.

So, the answer will be APY = 3.649%