Question

Suppose a savings and loan pays a nominal rate of 1.21.2​% on savings deposits. Find the effective annual yield if interest is compounded 10 comma 00010,000 times per year?

Answer 1

1.21%

Explanation:

We have been given that a savings and loan pays a nominal rate of 1.2​% on savings deposits. We are asked to find the effective annual yield, when interest is compounded 10 comma 00010,000 times per year.

We will use Annual Percentage Yield formula to solve our given problem.

`APY=(1+(r)/(n))^n-1`, where,

r = Annual interest rate in decimal form,

n = Number of times interest is compounded per year.

`1.2\%=(.2)/(100)=0.012`

`APY=(1+(0.012)/(10,000))^(10,000)-1`

`APY=(1+0.0000012)^(10,000)-1`

`APY=(1.0000012)^(10,000)-1`

`APY=1.0120722815791632-1`

`APY=0.0120722815791632`

`0.0120722815791632* 100\%=1.20722815791632\%\approx 1.21\%`

Therefore, the effective annual yield would be 1.21%.