Simple Interest
Math MCQs

Question :  ( 1 of 10 )  How much loan did Deborah borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8940 to clear it?

Correct Answer  $7450

Solution & Explanation

Solution

Given,

Amount (A) = $8940

Rate of Simple Interest (R) = 4%

Time (T) = 5 years

Thus, Principal (P) = ?

Method (1) Using Formula

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

Formula to find the Principal (P)

Amount (A) = Principal (P) + Principal (P) × Rate (R) × Time (T)

⇒ Amount (A) = Principal (P) [1 + Rate (R) × Time (T)]

⇒ A = P (1 + RT)

Using the formula to find the Amount (A), the fourth can be calculated if any three of A, P, R, and T are given

In the given question, we need to find the Principal (P)

Therefore, by substituting, Amount, Rate, and Time, in the formula A = P (1 + RT) we get

$8940 = P (1 + 4% × 5)

⇒ $8940 = P (1 + ⁴/₁₀₀ × 5)

⇒ $8940 = P (1 + ^{4 × 5}/₁₀₀)

⇒ $8940 = P (1 + ²⁰/₁₀₀)

⇒ $8940 = P (^{100 + 20}/₁₀₀)

⇒ $8940 = P × ¹²⁰/₁₀₀

⇒ P × ¹²⁰/₁₀₀ = $8940

⇒ P = ⁸⁹⁴⁰/_¹²⁰/100

⇒ P = 8940 × ¹⁰⁰/₁₂₀

⇒ P = ^{8940 × 100}/₁₂₀

⇒ P = ⁸⁹⁴⁰⁰⁰/₁₂₀

⇒ P = $7450

Thus, the sum borrowed (P) = $7450 Answer

Method (1) Using Unitary Method

Calculation of the Principal using unitary method when Amount, Time and Rate of Simple Interest are given

Calculation of the Simple Interest

Let, the principal = 100

Here, since rate of simple interest = 4% per annum

Thus, Interest = 4% of principal

⇒ Interest = 4% of 100 = 4

Thus, Simple Interest for 1 year = 4

Calculation of the Amount

Since, in the question, time = 5 years

So, we need to calculate the simple interest for the given time period, which is 5 years

Thus, Simple Interest for 5 years = 5 × Simple Interest for 1 year

= 5 × 4 = 20

Thus, simple interest for 5 years = 20

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 20 = 120

Calculation of the Principal

Now,

∵ If the Amount is 120, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₂₀

∴ If the Amount is 8940, then the Principal = ¹⁰⁰/₁₂₀ × 8940

= ^{100 × 8940}/₁₂₀

= ⁸⁹⁴⁰⁰⁰/₁₂₀

= 7450

Thus, Principal = $7450

Thus, the sum borrowed = $7450 Answer

Similar Questions

(1) Thomas took a loan of $5600 at the rate of 10% simple interest per annum. If he paid an amount of $8960 to clear the loan, then find the time period of the loan.

(2) William took a loan of $5000 at the rate of 8% simple interest per annum. If he paid an amount of $7400 to clear the loan, then find the time period of the loan.

(3) Calculate the amount due after 9 years if John borrowed a sum of $5200 at a rate of 6% simple interest.

(4) Calculate the amount due if Mary borrowed a sum of $3050 at 3% simple interest for 4 years.

(5) Mark took a loan of $6800 at the rate of 10% simple interest per annum. If he paid an amount of $10880 to clear the loan, then find the time period of the loan.

(6) If Jessica borrowed $3750 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.

(7) Elizabeth took a loan of $4900 at the rate of 7% simple interest per annum. If he paid an amount of $7987 to clear the loan, then find the time period of the loan.

(8) Calculate the amount due after 9 years if Robert borrowed a sum of $5100 at a rate of 3% simple interest.

(9) What amount will be due after 2 years if James borrowed a sum of $3000 at a 6% simple interest?

(10) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 2% simple interest?