a man has \$43000 in a IRA mutual fund and \$37000 in a money market account that pays %5 less. What is the rate of return for each account if his total annual interest income is \$4750?

Subject
Topic
Level
Highschool
9

I1= 43000 x I ( the annual interest of 43000\$ )

I2= 37000 ( I- 5%) = 37000 ( 0,95 I ) ( the annual interest of 37000\$ )

I1 + I2 = 4750 ( the total interest of the year for both amount (43000\$ and 37000\$)

By placing the value of I1 and I2 in the equation of the total year interest:

43000 I + 35150 I = 4750

78150 I = 4750

I = 4750 / 78150 = 6.078% ( we have obtained the annual rate percentage for both amount)

Now to find the annual interest of every amount we need:

First to place the value of I in the 43000\$ interest equation:

I1 = 43000 x 6.078% = 2613,56

Second to place the value of I in the 37000\$ interest equation:

I2 = 37000 x (0.95x6.078%) = 37000 x 5.774% = 2136,42

To make sure that the % rate obtained was the correct answer:

I+ I= 2613,56 + 2136,42 = 4749,98 approximately 4750\$

As a result: the rate for 43000 \$ is 6.078% and the rate of 37000 \$ is 5.774%