Question

two equal sums were lent at simple interest for 4 years and 3 years respectively the rate of interest on the letter was 3% higher than that on the former, but the amount in each case 1088 find the sum and the rate ?
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Answer 1

Answer:

Step-by-step explanation:

Year 4:

• Future sum = 1088
• Present sum = p
• Interest rate = i
• Number of years = 4

Year 3:

• Future sum = 1088
• Present sum = p
• Interest rate = i + 0.03
• Number of years = 3

Future sum = (Present Sum)(Interest Rate)(Number of Years)

Year 4 -> 1088 = (p)(i)(4)

Year 3 -> 1088 = (p)(i+0.03)(3)

Solving for i:

1. Set Year 4 equation and Year 3 equation to each other because they both equal 1088.

(p)(i)(4) = (p)(i+0.03)(3)

2. Divide both sides by p to cancel p.

(i)(4) = (i +0.03)(3)

3. Multiply out both sides.

4i = 3i + 0.09

4. Subtract both sides by 3i.

i = 0.09 = 9%

For Year 4:

i = 0.09 = 9%

For Year 3:

i = (0.09 + 0.03) = 0.12 = 12%

Solving for p:

1088 = (p)(0.09)(4)

3022.22 = p

Summary:

Present sum = $3022.22

Interest rate year 3 = 12%

Interest rate year 4 = 9%