Question

Aleksandra Tomich invested $ 6 comma 936 comma part at 4 % simple interest and part at 2 % simple interest for a period of 1 year. How much did she invest at each rate if each account earned the same​ interest?

Answer 1

Answer:

$4,624 was invested at 2%

$2,312 was invested at 4%

Explanation:

We want the product of interest rate and amount invested to be the same for both accounts. That means the account with twice the interest rate has half the amount of money in it that the other account has.

When the account balances are in the ratio 1:2, the account with the smaller balance has 1/(1+2) = 1/3 of the total amount invested. The account with the larger balance has the other 2/3 of the total amount invested.

In the 2% account, the invested amount is (2/3)·$6936 = $4624.

In the 4% account, the invested amount is (1/3)·$6936 = $2312.