Question

(1 pt) Rhonda deposits  dollars in an account paying 8.2 percent effective, and at the same time also deposits  dollars in another account paying 9.2 percent effective. After 9 years have passed, the combined total in the two accounts is 58000 dollars. In another 2 years, the balance in the account paying 9.2 percent effective is three times that of the other account. What is the balance in the account paying 8.2 percent effective 14 years after the initial deposit?
Answer =  dollars.

Can use excel as long as answer is correct

Answer 1

	Account-1	Account-2
Interest	8.20%	9.20%
Time period in years	9	9
Initial deposit	X	Y
Amount after 9 years	X*(1+8.2%)^9	Y*(1+9.2%)^9
As per question
X*(1+8.2%)^9+Y*(1+9.2%)^9=58000
X*(1+8.2%)^9=	58000-Y*(1+9.2%)^9
Amount after 11 years	X*(1+8.2%)^11	Y*(1+9.2%)^11
As per question
Y*(1+9.2%)^11=	(X*(1+8.2%)^11)*3
Y*(1+9.2%)^11=	(X*(1+8.2%)^11)*3
Y*(1+9.2%)^11=	((X*(1+8.2%)^9)*(1+8.2%)^2)*3
Y*(1+9.2%)^11=	((58000-Y*(1+9.2%)^9)*(1+8.2%)^2)*3
( Y*(1+9.2%)^11)/3=	((58000-Y*(1+9.2%)^9))*(1+8.2%)^2)
Y*0.8776=	58000*(1+8.2%)^2 - Y*(1+9.2%)^9*(1+8.2%)^2)
Y*0.8776=	58000*(1+8.2%)^2 - Y*(1+9.2%)^9*(1+8.2%)^2)
Y*0.8776=	67901.992- Y*2.5849
Y*0.8776+ Y*2.5849=	67901.992
3.4626*Y=	67901.992
Y=	=67901.992/3.4626
Y=	$             19,609.84
X*(1+8.2%)^9=	58000-19609.84*(1+9.2%)^9
X*(1+8.2%)^9=	14,701.01
X=	14701.01/(1+8.2%)^9
X=	$               7,232.72
Amount of First account after 14 years
Required amount=	7232.72*(1+8.2%)^14
Required amount=	$             21,801.38