You deposit $5,000 in an account earning 5% interest compounded semi-annually for 2 years and 7% interest compounded quarterly thereafter. What is the account value after 7 years

The account value after 7 years will be 7,808.

Explanation:

First we have to find out the account value after 2 years. The interest rate is 5% but it is compounded semi annually so we will divide it by 2

Interest Rate = 2.5%

It is a 2 year period but it is semi annual so there will be 4 compounding periods.

We will use the compound interest formula.

P (1+R) ^N

P=5,000

R=2.5

N = 4

1.025^4*5000=5519

Now we have to find the account value at the end of 7 years, since 2 years have already passed only 5 years remain. The interest rate for the last 5 years is 7% but it is compounded quarterly so we will divide it by 4 7/4=1.75. Also the number of compounding periods will be 5*4=20

P=5519

R=1.75

N=20

1.0175^20*5519=7,808.