Question

A man invests 16,500 pesos in two kinds treasury notes, which yield 7.5% and 6% annually. After two years year, he earns 2,442 pesos in interest. How much does he invest at the 6 % rate?​

Answer 1

Answer:

Formula for simple interest is

I  =  Prt 

Here, P  =  5000, t  =  4, r  =  6%

Let us plug these values in the above formula

I  =  5000 ⋅ 6/100 ⋅ 4

I  =  1200

The formula to find the accumulated value is 

=  Principal + Interest 

=  5000 + 1200

=  6200

Hence, the value of his deposit after 4 years is $6,200.

Answer 2

The invested amount of 1100 pesos at the 6% rate.

Given,

A man invests 16,500 pesos in two kinds treasury notes, which yield 7.5% and 6% annually. After two years year, he earned 2,442 pesos in interest.

To Find,

The amount invested by the man at the 6% rate.

Solution,

Let x be the amount invested at a 6% rate.

Then, the amount invested in 7.5% account = 16500 - x

After two years, the total interest earned in both accounts is 2,442 pesos.

⇒ Interest at 6% rate + Interest at 7.5% rate = 2442

⇒ x ⋅ 6/100 ⋅ 2 + (16500 - x) ⋅ 7.5/100 ⋅ 2 = 2442

⇒ x ⋅ 0.06 ⋅ 2 + (16500 - x) ⋅ 0.075 ⋅ 2 = 2442

⇒ 0.12x + (16500 - x) ⋅ 0.15 = 2442

⇒ 0.12x + 2475 - 0.15x = 2442

⇒ 2475 - 0.03x = 2442

⇒ 2475 - 2442 = 0.03x

⇒ 33 = 0.03x

Divide both sides by 0.03.

⇒ 33/0.03 = x

⇒ 3300/3 = x

On dividing, we get the value of x,

1100 = x

Hence, the amount invested at a 6% rate is 1100 pesos.

The invested amount of 1100 pesos at the 6% rate.

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