Question

a $7,000 principal is invested in two accounts, one earning 3% interest and another earning 7% interest. if the total interest for the year is $262, then how much is invested in each account?

Answer 1

Let the investment in first account be x and this account is earning 3% interest

So Interest on this account is 3% of x = 0.03x

So the investment in second account would be (7000-x) and this account is earning 7% interest

So the interest on this account is 7% of (7000-x) = 0.07*(7000-x)

Given that total interest for the year is $262

So we have

0.03x + 0.07(7000-x) = 262

0.03x - 0.07x + 0.07*7000 = 262

-0,04x + 490 = 262

-0.04x = 262-490

-0.04x = - 228

0.04x = 228x

x = 228/0.04

x = 5700

Therefore Investment in one account s 5700 and the investment in other account is 7000-5700 = 1300

Answer 2

The amount invested in the account that gives $3\%$ interest rate is $\boxed{\ 5700}$ and the amount invested in the account that gives $7\%$ is $\boxed{\ 1300}.$

Further explanation:

The compound interest rate formula can be expressed as follows,

$\boxed{A = P{{\left( {1 + i} \right)}^n}}$

Here, A represents the amount, P represents the principal amount, i represent the interest rate and n represents the time.

Given:

The principal amount in the two account is $\ 7000.$

The interest rate in the first account is $3\%$ and the interest rate in the second account is $7\%.$

The total interest earned is $\ 262.$

Explanation:

Consider x be the amount invested in the account that gives $3\%$ interest rate.

Therefore, the amount invested in the account that gives $7\%$ interest rate is $7000-x$

The total interest is $\ 262.$

The amount can be calculated as follows,

$\begin{aligned}0.03x + 0.07\left({7000 - x}\right)&=262\\0.03x + 490 - 0.07x &= 262\\- 0.04x &= 262 - 490\\- 0.04x&=  - 228\\x&=\frac{{228}}{{0.04}}\\x&= 5700\\\end{aligned}$

The amount invested in the account that gives $3\%$ interest rate is $\ 5700.$

The amount invested in the account that gives $7\%$ interest rate can be calculated as follows,

$\begin{aligned}{\text{Amount}&= 7000 - 5700\\&= 1300\\\end{aligned}$

The amount invested in the account that gives $3\%$ interest rate is $\boxed{\ 5700}$ and the amount invested in the account that gives $7\%$ is $\boxed{\ 1300}.$

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Answer details:

Grade: High School

Subject: Mathematics

Chapter: Interest rate

Keywords: Principal, invested, interest rate, account, two accounts, 3% interest rate, 7% interest rate, total interest in a year, $262, invested amount, each account.