Question

A passbook savings account has a rate of 7%. Find the effective annual yield, rounded tonthe nearest tenth of a percent, if the interest is compounded semiannually.

Answer 1

There are 2 halves in a year in case of semi anually

Therefore n= 2

The effective annual yield can be calculated using the formula;

$y=(1+\frac{r}{n})^n-1$

where r is the rate

n = 2 and r = 7% = 0.07

$y=(1\text{ + }\frac{0.07}{2})^2-1$$y\text{ = (1 + }0.035)^2-\text{ 1}$$y=(1.035)^2-\text{ 1}$$y\text{ = 1.071225-1}$$y\text{ = 0.071225}$

The effective annual yield is y ≈ 0. 1 to the nearest tenth

The above is in decimal form

We can convert to percentage form by multiplying by 100% and we will have;

y = 0.071225 x 100% = 7. 1 %

EFFECTIVE ANNUAL YIELD IS 7.1%