Simple Interest
Math MCQs

Question :    Find the amount to be paid if Susan borrowed a sum of $5650 at 10% simple interest for 8 years.

Correct Answer  $10170

Solution & Explanation

Solution

Given,

Principal (P) = $5650

Rate of Simple Interest (SI) = 10%

Time (t) = 8 years

Thus, Amount (A) = ?

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

Thus, here 10% simple interest means, Rate of Simple Interest (SI) is 10% 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) = $5650 × 10% × 8

= $5650 ×¹⁰/₁₀₀ × 8

= ^{5650 × 10 × 8}/₁₀₀

= ^{56500 × 8}/₁₀₀

= ⁴⁵²⁰⁰⁰/₁₀₀

= $4520

Thus, Simple Interest = $4520

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 = $5650 + $4520

= $10170

Thus, Amount to be paid = $10170 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 = $5650

Rate of Simple Interest (SI) or (R) = 10%

And, Time (t) = 8 years

Thus, Amount (A)

= $5650 + ($5650 × 10% × 8)

= $5650 + ($5650 ×¹⁰/₁₀₀ × 8)

= $5650 + (^{5650 × 10 × 8}/₁₀₀)

= $5650 + (^{56500 × 8}/₁₀₀)

= $5650 + (⁴⁵²⁰⁰⁰/₁₀₀)

= $5650 + $4520 = $10170

Thus, Amount (A) to be paid = $10170 Answer

Method (3) Unitary Method

Calculation of Amount using Unitary Method

Calculation of Interest using Unitary Method

Here, given Rate of Simple Interest = 10%

This, means, $10 per $100 per year

∵ For $100, the simple interest for 1 year = $10

∴ For $1, the simple interest for 1 year = ¹⁰/₁₀₀

∴ For $5650, the simple interest in 1 year

= ¹⁰/₁₀₀ × 5650

= ^{10 × 5650}/₁₀₀

= ⁵⁶⁵⁰⁰/₁₀₀ = $565

Thus, simple interest for 1 year = $565

Therefore, simple interest for 8 years

= Simple interest for 1 year × 8

= $565 × 8 = $4520

Thus, Simple Interest (SI) = $4520

Calculation of Amount

Amount = Principal + Interest

Thus, Amount = $5650 + $4520

= $10170

Thus, Amount to be paid = $10170 Answer

Similar Questions

(1) What amount will be due after 2 years if Thomas borrowed a sum of $3400 at a 10% simple interest?

(2) Sarah took a loan of $5700 at the rate of 10% simple interest per annum. If he paid an amount of $10830 to clear the loan, then find the time period of the loan.

(3) What amount does Elizabeth have to pay after 6 years if he takes a loan of $3450 at 2% simple interest?

(4) If Anthony paid $5160 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(5) John took a loan of $4400 at the rate of 7% simple interest per annum. If he paid an amount of $7172 to clear the loan, then find the time period of the loan.

(6) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 8% simple interest?

(7) Joseph took a loan of $5400 at the rate of 8% simple interest per annum. If he paid an amount of $8856 to clear the loan, then find the time period of the loan.

(8) Matthew took a loan of $6400 at the rate of 8% simple interest per annum. If he paid an amount of $9472 to clear the loan, then find the time period of the loan.

(9) Find the amount to be paid if William borrowed a sum of $5500 at 10% simple interest for 7 years.

(10) Michael took a loan of $4600 at the rate of 7% simple interest per annum. If he paid an amount of $6854 to clear the loan, then find the time period of the loan.