You deposit 1000 in an account that pays 7 interest compound

You deposit $1000 in an account that pays 7% interest compounded semiannually. After 4 years, the interest rate is increased to 7.44% compounded quarterly, what will be the value of the account after 8 years? The value of the account will be $ (Round to the nearest dollar as needed.)

Solution

The value of account will be $1769

Future Value = Present Value * ( 1+ Interest rate )^ Number of periods

Value of Account after 4 years:

Present Value = 1000

Interest rate = 0.07/2 = 0.035 (Compounded semiannually)

Period = Number of years *2 = 4*2 = 8

Value of Account after 4 years = 1000(1.035)^8

= 1000 * 1.317

=1317

Value of Account After next 4 years (5-8)

Future Value = Present Value * ( 1+ Interest rate )^ Number of periods

Present Value = 1317

Interest rate = 0.0744/4 = 0.0186 (Compounded quarterly)

Period = Number of years *4 = 4*4 = 16

Value of Account after 4 years = 1317(1.0186)^16

= 1317 * 1.34295 = 1769