interest rate

[niyt]

A person invested $25,200 in two accounts, which pay 5 % and 10% interest annually. The amount invested at 10% rate is 110% of the amount invested at 5% rate. After three years year, he earns $2,442 in interest. How much did he invest at the 5% rate ?
I have the answer, but it does not make sense to me (x=12000)
Thank you

 

[stapel]

What have you tried? Where are you getting stuck?

For instance, since the amount invested in the high-interest (and thus more risky) account is defined in terms of the amount invested in the safer account, you picked a variable for the amount in the safer account and then created an expression for the amount in the risky account. What variable did you pick, and what expression did you create?

You then plugged these into the simple-interest formula. What expressions did you get?

You then summed the two interest expressions, and set this sum equal to the given amount. What equation did you get?

You then solved this linear equation for the value of the variable. What value did you get?

And so forth.

Please be complete. Thank you!

 

[The Highlander]

A person invested $25,200 in two accounts, which pay 5 % and 10% interest annually. The amount invested at 10% rate is 110% of the amount invested at 5% rate. After three years year, he earns $2,442 in interest. How much did he invest at the 5% rate ?
I have the answer, but it does not make sense to me (x=12000)
Thank you

It strikes me that you may not have reproduced the question correctly. Can you please post the question in its entirety as it was posed in its original form (a picture would be preferable).

I say this because the “answer” that you appear to offer for the sum invested in the account with the 5% annual return: “(x=12000)” if that is, indeed, meant to be the sum invested in that account makes perfect sense (given the way you have worded the original question) but, that would be the correct amount regardless of the interest rates or the interest earned after any amount of time!

$12,000 + $13,200 (110% of $12,000 ie: $12,000 × 1.10) = $25,200.​

The second sentence (as you present it) alone determines this, without any of the following “nonsense” about interest earned after three years:

Let x be the amount invested in the lower interest rate account, then the amount invested in the higher rate account is 1.1x (ie: 110% of x) thus x+1.1x=25,200 \(\displaystyle \Rightarrow\) 2.1x=25,200 \(\displaystyle \Rightarrow\)x=25,200÷2.1=12,000.

So, unless the question has been specifically designed to confuse you by including the “nonsense” about the interest rates & interest earned (which seems unlikely) then that leads me to suspect that you haven’t provided an accurate version of the original question.

I say “nonsense” because the interest earned on $12,000 @ 5% pa over three years would be $1,891.50 not $2,442 and even if the interest earned figure is supposed to be the total earned by both accounts (your wording does not make that clear) that wouldn’t come to $2,442 either! Even if the whole $25,200 had been invested in the lower return account the interest would exceed $2,442 over three years! ($3,972.15 or $3,780 without compounding.)

Please repost the entire question in its original format (even if it’s not in English) so we can see what the real problem is here.