Question

You would like to deposit $1000 in a savings account. The bank gives you two options: Account A pays interest at a rate of 8% (annually compounded) each year. Account B pays a simple interest rate of 8% per year (but never compounds), and gives you a $50 bonus at the end of 5 years. What is the difference in the account balances in 5 years? (Your answer should be the solution to Balance of Account A minus Balance of Account B.)

Answer 1

Balance in Account A					$ 1,469.33
Minus Balance in Account B					$ 1,450.00
Difference in the account balances in 5 years					$       19.33
Working:
# 1	Account balance in 5 years			=	P*(1+i)^n		Where,
	(Option A)			=	1000*(1+0.08)^5		P	$       1,000
				=	$ 1,469.33		i	8%
							n	5
# 2	Account balance in 5 years			=	Investment + Interest Earned + Bonus
	(Option B)			=	1000+(1000*8%*5)+50
				=	$ 1,450.00