Question

a student invested $10,000 received an inheritance in three parts. with one person she brought mutual funds that offered and returned a 4% per year. the second part which amounted to twice the first was used to buy a government bonds paying 4.5% per year. she put the rest into a savings account that paid 2.5% annual interest. during the first year the total interest was $415. how much did she invest in each rate?​

Answer 1

The amount invested at 4% per year was $3,000

The amount invested at 4.5% per year was $6,000

The amount invested at 2.5% per year was $1,000

Explanation:

Let

x -----> the amount invested at 4% per year

2x ----> the amount invested at 4.5% per year

10,000-3x -----> the amount invested at 2.5% per year

we know that

The interest earned by the amount invested at 4% per year plus the interest earned by the amount invested at 4.5% per year plus the interest earned by the amount invested at 2.5% per year must be equal to $415

so

`4\%=4/100=0.04`

`4.5\%=4.5/100=0.045`

`2.5\%=2.5/100=0.025`

`0.04x+0.045(2x)+0.025(10,000-3x)=415`

Solve for x

`0.04x+0.09x+250-0.075x=415`

`0.055x=415-250`

`0.055x=165`

`x=\$3,000`

therefore

The amount invested at 4% per year was $3,000

The amount invested at 4.5% per year was $6,000

The amount invested at 2.5% per year was $1,000