Last year, Amanda had $10,000 to invest. She invested some of it in an account that paid 10% simple interest per year, and she invested the rest in an account that paid 5% simple interest per year. After one year, she received a total of $950 in interest. How much did she invest in each account?

 

Amanda invested $ 9000 in the account earning 10 % interest rate. 

 

Amanda invested $ 1000 in the account earning 5 % interest rate.

Step-by-step explanation

 

We have to solve the given problem using the concept of simple interest. 

 

We have the Formula for the Interest earned(I) is given as

 

I=P×r×t

 

where, 

 

P = the principal amount deposited. 

 

r = the interest rate is given in decimals. (To convert percentage into decimals, we need to divide with 100 %). 

 

and t= the time in years. 

 

 

So Using this concept we have to solve our given problem using the given details.

 

 

Amanda initially has $ 10000 to invest. 

 

She Invests some amount of money in an account with an interest rate of 10 %.  and remaining portion money in an account with an interest rate of 5%. 

 

So, 

 

Let's, 

 

 x = the amount Amanda invested in the account earning 10 %. ----------(Account 1 )

 

and, the amount invested in the account earning 5 % will be (10000-x). Because she invested a total of 10000 in both accounts.

 

So,

 

 (10000-x)=  the amount Amanda invested in the account earning 5 %. --------(Account 2)

 

 

 

 

 

 

Now we have to use our formula for the total interest earned in both accounts. 

 

Now we have to create a formula for the interest earned in the account earning 10%. 

 

Account 1 

 

 

We have, 

 

 I=P×r×t

 

The Principal amount (P) = x 

 

Interest rate (r) = 0.1 (Because, We have to divide the given interest rate of 10 %. by dividing with 100%. That is, r=10010?=0.1)

 

and we have the time(t) is 1 year. So, t= 1

 

 

So we have to substitute these value in our formula, 

 

Total interest earned(I) = P×r×t

 

Total interest earned(I) = (x×0.1×1)=0.1x

 

So we have obtained, 

 

The total interest earned in the account earning 10 % = 0.1x

 

 

Now we have to use the interest earned formula in the account earning 5 % of the interest rate. 

 

Account 2

 

We have, 

 

I=P×r×t

 

The principal amount (P) =( 10000-x)

 

Interest rate (r) = 0.05 (Because, We have to divide the given interest rate of 5 %. by dividing with 100%. That is, r=1005?=0.05)

 

and we have the time (t) is 1 year. So t = 1

 

Now we have to substitute these value in our formula, 

 

Total interest earned(I) = P×r×t

 

Total interest earned(I) = (10000−x)×0.05×1

 

I=0.05(10000−x)

 

I=(0.05×10000−0.05x)

 

I=(500−0.05x)

 

So we have obtained, 

 

The total interest earned in account earning 5 % = (500-0.05x)

 

 

 

Now we have given that Amanda earned $950 interest from both accounts. 

 

 

(Interest rate from account earning 10 % )+( interest rate from account earning 5 % )= $ 950

 

 

Now we have to substitute the equations we have obtained,

 

 The total interest earned in the account earning 10 % = 0.1x

 

The total interest earned in account earning 5 % = (500-0.05x)

 

 

So, 

 

Our relation for the interest earned can be equated as 

 

(Interest rate from account earning 10 % )+( interest rate from account earning 5 % )= $ 950

 

 

 

( 0.1x) + ( 500 -0.05x) = 950

 

( 0.1x + 500-0.05x) = 950

 

(0.05x + 500) = 950

 

0.05x = 950-500

 

0.05x = 450

 

x=0.05450?=9000

 

So, The Amount invested in the account earning 10 %  (x)= $9000.

 

Then the amount invested in the account earning 5 % interest rate = ( 10000-x) 

 

 Or, The amount invested in the account earning 5 % interest rate  = ( 10000-9000) = 1000

 

So, The Amount invested in the account earning 5 %  = $1000.

 

 

 

 

So we have Solved that,

 

 Amanda invested $ 9000 in the account earning 10 % interest rate. 

 

and, Amanda invested $ 1000 in the account earning 5 % interest rate.

 

 

 

we have completed Our Solution. you can ask your doubts in the comment section, I'll help you :)