Question

You have just deposited $13,000 into an account that promises to pay you an annual interest rate of 6.9 percent each year for the next 5 years. You will leave the money invested in the account and 15 years from today, you need to have $43,590 in the account. What annual interest rate must you earn over the last 10 years to accomplish this goal?

Answer 1

Interest rate in last 10 years must be 9.16%

Step-1:Future value of investment in next 5 years
Future value	=	Investment now	*	Future value of 1
	=	$       13,000	*	1.39601
	=	$ 18,148.13
Working:
Future value of 1	=	(1+i)^n		Where,
	=	(1+0.069)^5		i	=	6.90%
	=	1.39600999		n	=	5
Step-2:Calculation of required interest rate in last 10 years
A		=	P*(1+i)^n		Where,
$ 43,590.00		=	18148.13*(1+i)^10		A	Future value	=	$ 43,590.00
2.40190038		=	(1+i)^10		P	Current value	=	$ 18,148.13
2.40190038	^(1/10)	=	1+i		i	Interest rate	=	?
1.09157982		=	1+i		n	Time	=	10
0.09157982		=	i
So, Interest rate will be		9.16%