Simple Interest
Math MCQs

Question :    Find the amount to be paid if Patricia borrowed a sum of $5150 at 9% simple interest for 7 years.

Correct Answer  $8394.5

Solution & Explanation

Solution

Given,

Principal (P) = $5150

Rate of Simple Interest (SI) = 9%

Time (t) = 7 years

Thus, Amount (A) = ?

The Rate of Interest is always calculated per annum, i.e. per year.

Thus, here 9% simple interest means, Rate of Simple Interest (SI) is 9% per annum.

Method (1) Using Formula

Calculation of Simple Interest

Formula to Calculate Simple Interest

Simple Interest (SI) = Principal × Rate × Time

Thus, Simple Interest (SI) = $5150 × 9% × 7

= $5150 ×⁹/₁₀₀ × 7

= ^{5150 × 9 × 7}/₁₀₀

= ^{46350 × 7}/₁₀₀

= ³²⁴⁴⁵⁰/₁₀₀

= $3244.5

Thus, Simple Interest = $3244.5

Calculation of Amount

The total money paid to the lender by a borrower is called the Amount.

In other words, sum of priciple and interest is called the Amount.

Formula to Calculate the Amount

Amount = Principal + Interest

Thus, Amount = $5150 + $3244.5

= $8394.5

Thus, Amount to be paid = $8394.5 Answer

Method (2)

Calculation of Amount when Principal, Rate of Simple Interest and Time are given

Calculation of Amount directly using Principal, SI, and Time

Formula to calculate the Amount

Amount (A) = Principal (P) + Principal(P) × Rate of Interest (SI) × Time (t)

⇒ A = P + PRT

Here in the question, P = $5150

Rate of Simple Interest (SI) or (R) = 9%

And, Time (t) = 7 years

Thus, Amount (A)

= $5150 + ($5150 × 9% × 7)

= $5150 + ($5150 ×⁹/₁₀₀ × 7)

= $5150 + (^{5150 × 9 × 7}/₁₀₀)

= $5150 + (^{46350 × 7}/₁₀₀)

= $5150 + (³²⁴⁴⁵⁰/₁₀₀)

= $5150 + $3244.5 = $8394.5

Thus, Amount (A) to be paid = $8394.5 Answer

Method (3) Unitary Method

Calculation of Amount using Unitary Method

Calculation of Interest using Unitary Method

Here, given Rate of Simple Interest = 9%

This, means, $9 per $100 per year

∵ For $100, the simple interest for 1 year = $9

∴ For $1, the simple interest for 1 year = ⁹/₁₀₀

∴ For $5150, the simple interest in 1 year

= ⁹/₁₀₀ × 5150

= ^{9 × 5150}/₁₀₀

= ⁴⁶³⁵⁰/₁₀₀ = $463.5

Thus, simple interest for 1 year = $463.5

Therefore, simple interest for 7 years

= Simple interest for 1 year × 7

= $463.5 × 7 = $3244.5

Thus, Simple Interest (SI) = $3244.5

Calculation of Amount

Amount = Principal + Interest

Thus, Amount = $5150 + $3244.5

= $8394.5

Thus, Amount to be paid = $8394.5 Answer

Similar Questions

(1) Margaret took a loan of $6700 at the rate of 9% simple interest per annum. If he paid an amount of $12730 to clear the loan, then find the time period of the loan.

(2) Charles had to pay $4134 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(3) Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 9% simple interest.

(4) What amount will be due after 2 years if Anthony borrowed a sum of $3650 at a 8% simple interest?

(5) What amount will be due after 2 years if Richard borrowed a sum of $3300 at a 4% simple interest?

(6) Michael took a loan of $4600 at the rate of 6% simple interest per annum. If he paid an amount of $7084 to clear the loan, then find the time period of the loan.

(7) Michael took a loan of $4600 at the rate of 8% simple interest per annum. If he paid an amount of $7544 to clear the loan, then find the time period of the loan.

(8) Find the amount to be paid if Richard borrowed a sum of $5600 at 8% simple interest for 8 years.

(9) Thomas took a loan of $5600 at the rate of 8% simple interest per annum. If he paid an amount of $8288 to clear the loan, then find the time period of the loan.

(10) In how much time a principal of $3200 will amount to $3680 at a simple interest of 5% per annum?