# Understanding/Calculate effective annual rate and savings

I came across the following exercise:

You put \$1000 into a savings account today that offers a 5% APR with semi-annual compounding.

1. What is the effective annual rate of the saving account?
2. How much money will you have in the account after 2 years?

I could choose from the following answer options:

1. 0.1025, 0.0975, 1.1025, 0.0250
2. 814.5, 1102.5, 1215.51, 902.5

My calculation:

For 1.: Using following formula:

``````EAR = (1 + APR/k)^k - 1, where APR = 0.05 and k=2
``````

My result EAR = 5.06% which is clearly not one of the possible answers. So where is my mistake?

For 2.: I calculated the FV after two years using above EAR.

``````FV(1000) = 1000*(1+EAR)^2 = 1115.14
``````

which is again clearly not one of the possible answers.

I know that 2 has to be a consequential error, because 1. is not correct. So I would highly appreciate it if anyone could explain to me what I should have done.

• The exact definition of APR is location-dependent. Mar 13, 2022 at 7:26