Question

$5,000 is deposited today into a bank account. The account earns 6.2% per annum compounded half yearly for the first 7 years, then 6.1% per annum compounded quarterly thereafter. Assuming no further deposits or withdrawals are made,

(d) Calculate the account balance 10 years from today.

Answer 1

We would use the future value to calculate the account balance 10 years from today.
Annual effective interest rate for first 7 years
Annual effective interest rate	(1+(0.062/2))^2 - 1
Annual effective interest rate	6.30%
Annual effective interest rate subsequently.
Annual effective interest rate	(1+(0.061/4))^4 - 1
Annual effective interest rate	6.24%
Formula to calculate future value
Future value	Amount deposited*(1+interest rate)^no of years
Calculation of future value at end of 7 years
Future value	5000*((1+0.0630)^7)
Future value	$7,666.40
Calculation of future value at end of 10 years of $7,666
Future value	5000*((1+0.0624)^3)
Future value	$9,193.21
Thus, account balance 10 years from today is $9,193.21.