Question

Aaron invested a total of $4,100, some in an account earning 8% simple interest, and the rest in an account earning 5% simple interest. How much did he invest in each account if after one year he earned $211 in interest?

Select one: a. $200 at 8%, $3,900 at 5% b. $3,200 at 8%, $900 at 5% c. $900 at 8%, $3,200 at 5% d. $3,900 at 8%, $200 at 5%

Answer 1

Answer: He invest $200 at 8%, $3,900 at 5% .

Step-by-step explanation:

Let P be the amount Aaron invested in account with 8% simple interest then 4100-P denote the amount Aaron invested in account with 5% simple interest .

We know that the simple interest with rate r% for t years is given by:-

$S.I.=P\frac{r}{100}t$

It si given that after 1 year total interest = !211

Then, $P\frac{8}{100}(1)+(4100-P)\frac{5}{100}=211\\\Rightarrow0.08P+0.05(4100)-0.05P=211\\\Rightarrow0.03P+205=211\\\Rightarrow0.03P=211-205\\\Rightarrow\ P=\frac{6}{0.03}\\\Rightarrow\ P=200$

4100-P=4100-200=3800

Hence, He invest $200 at 8%, $3,900 at 5% .