Question

1. You have $1000 to invest in two different accounts. To save the money you need for college, you need to average 5.7 percent interest. If the two accounts pay 4 percent and 6 percent interest, how much should you invest in each account? Options: A. $700 in 4%, $300 in 6% B. $550 in 4%, $450 in 6% C. $300 in 4%, $700 in 6% D. $150 in 4%, $850 in 6%

Answer 1

$150 in 4%, $850 in 6%

Explanation:

just took the test!

Answer 2

D. $150 in 4%, $850 in 6%

Explanation:

1. The amount available to invest in the accounts, A = $1,000

The amount of average interest rate needed = 5.7 percent = 0.057

The interest paid by one of the accounts, account 1, I₁ = 4 percent = 0.04

The interest paid by the other account, account 2, I₂ = 6 percent = 0.06

Let 'x' represent the amount invested in account 1 that pays 4% and let 'y' represent the amount invested in account 2, that pays 6% we get;

x + y = 1,000...(1)

0.04·x + 0.06·y = 0.057 × 1,000 = 57

∴ 0.04·x + 0.06·y = 57...(2)

Making 'y' the subject of equation (1) and (2), we have;

For equation (1), y = 1,000 - x...(3)

For equation (2), y = 950 - (2/3)·x...(4)

Subtract equation (4) from equation (3) gives;

y - y = 1,000 - x - (950 - (2/3)·x)

0 = 1,000 - 950 - x + (2/3)·x

0 = 50 - (1/3)·x

(1/3)·x = 50

x = 3 × 50 = 150

x = 150

The amount invested in the 4% account, x = $150

From equation (3), we have;

y = 1,000 - x

∴ y = 1,000 - 150 = 850

y = 850

The amount invested in the 6% account, y = $850.

Therefore;

$150 should be invested in the account that pays 4% while $850 should be invested in the account that pays 6%.