Simple Interest Problems

An investment of `16000 at 8% simple interest for 1 year and another investment at 18% simple interest for the same period, together fetch a return profit of 10% on the total investment. Find the total amount invested.

• `22000

• `20000

• `20500

• `18000

Answer explanation

The total investment is `20000. The first investment of `16000 at 8% yields `1280, and the second investment at 18% yields `720. Together, they return `2000, which is 10% of `20000.

If the simple interest on a certain sum for 15 months at 7.5% per annum exceeds the simple interest on the same sum for 8 months at 12.5% per annum by `32.50, then find the sum.

• `3000

• `3060

• `3120

• `2900

Answer explanation

Let the sum be P. The interest for 15 months at 7.5% is (P * 7.5/100 * 15/12) and for 8 months at 12.5% is (P * 12.5/100 * 8/12). Setting up the equation, we find P = 3120.

The simple interest received on a sum of money borrowed at the rate of 7% per annum in 2 years is the same as the amount received on a sum of `1750 in 4 years at the rate of 5% per annum. Find the amount.

• `1800

• `1600

• `2500

• `2400

Answer explanation

The simple interest for the second case is SI = 1750 * 5/100 * 4 = 350. For the first case, let the principal be P. SI = P * 7/100 * 2 = 0.14P. Setting them equal gives 0.14P = 350, so P = 2500. Thus, the amount is `2500.

A fixed sum of money was invested for 5 years at a fixed rate of simple interest. If had been invested at a 10% higher rate, it would have gained `2000 more. What was the principal invested?

• `3500

• `4000

• `4500

• `5000

Answer explanation

Let the principal be P. The interest for 5 years at rate r is (P*r*5)/100. At (r+10%), it is (P*(r+10)*5)/100. The difference is 2000. Solving gives P = 4000. Thus, the principal invested is `4000.

A sum at the end of 3 3/4 years at 6% simple interest per annum, yields a total amount of `2940 is received. What was the amount invested?

• `2,350

• `2,400

• `2,550

• `2,600

Answer explanation

To find the principal amount, use the formula A = P(1 + rt). Here, A = 2940, r = 0.06, and t = 3.75. Rearranging gives P = A / (1 + rt) = 2940 / (1 + 0.06 * 3.75) = 2400. Thus, the invested amount is `2,400.

The interest earned on the money invested for 6 years at a simple interest rate of 9.5% per annum was `456. What was the amount invested?

• `750

• `775

• `800

• `850

Answer explanation

To find the principal amount (P), use the formula for simple interest: I = P * r * t. Here, I = 456, r = 9.5% = 0.095, and t = 6. Rearranging gives P = I / (r * t) = 456 / (0.095 * 6) = 800. Thus, the amount invested is `800.

A sum of money becomes `457 in 5 years and `574 in 10 years at the same simple interest rate. Find the value (in rupees) of the sum.

• 500

• 280

• 340

• 420

Answer explanation

The difference in amounts over 5 years is `117, which is the interest for 5 years. Thus, the annual interest is `23.4. The principal can be calculated as `457 - (5 * 23.4) = `340.

On a certain sum, simple interest for 5 /2 years at an annual rate of 12% is `50 less than the interest on the same sum for 7 /2 years at an annual rate of 10%. Find the sum.

• `1,500

• `1,000

• `2,000

• `1,200

Answer explanation

Let the sum be P. The interest for 5.5 years at 12% is 0.12 * P * 5.5, and for 7.5 years at 10% is 0.10 * P * 7.5. Setting up the equation: 0.12 * P * 5.5 + 50 = 0.10 * P * 7.5 leads to P = 1000.

At the rate of 8% simple interest, a amount becomes `924 in 6 3/4 years. What amount was deposited initially.

• `626

• `650

• `600

• `675

Answer explanation

To find the principal amount (P), use the formula A = P(1 + rt). Here, A = 924, r = 0.08, and t = 6.75 years. Rearranging gives P = A / (1 + rt) = 924 / (1 + 0.08 * 6.75) = 600. Thus, the initial deposit was `600.

The difference between the interest on a sum of money at 12% per annum simple interest for 4 years and the same sum at 9% per annum simple interest for 5 years is `412.50. What is the amount?

• `13,900

• `14,630

• `14,080

• `13,750

Answer explanation

Let the principal be P. The interest difference is (P*12%*4) - (P*9%*5) = 412.50. Simplifying gives P = 13,750. Thus, the amount is `13,750.