Simple Interest
Math MCQs

Question :    If Joshua paid $5880 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

Correct Answer  $4900

Solution & Explanation

Solution

Given,

Amount (A) = $5880

Rate of Simple Interest (R) = 5%

Time (T) = 4 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

$5880 = P (1 + 5% × 4)

⇒ $5880 = P (1 + ⁵/₁₀₀ × 4)

⇒ $5880 = P (1 + ^{5 × 4}/₁₀₀)

⇒ $5880 = P (1 + ²⁰/₁₀₀)

⇒ $5880 = P (^{100 + 20}/₁₀₀)

⇒ $5880 = P × ¹²⁰/₁₀₀

⇒ P × ¹²⁰/₁₀₀ = $5880

⇒ P = ⁵⁸⁸⁰/_¹²⁰/100

⇒ P = 5880 × ¹⁰⁰/₁₂₀

⇒ P = ^{5880 × 100}/₁₂₀

⇒ P = ⁵⁸⁸⁰⁰⁰/₁₂₀

⇒ P = $4900

Thus, the sum borrowed (P) = $4900 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 = 5% per annum

Thus, Interest = 5% of principal

⇒ Interest = 5% of 100 = 5

Thus, Simple Interest for 1 year = 5

Calculation of the Amount

Since, in the question, time = 4 years

So, we need to calculate the simple interest for the given time period, which is 4 years

Thus, Simple Interest for 4 years = 4 × Simple Interest for 1 year

= 4 × 5 = 20

Thus, simple interest for 4 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 5880, then the Principal = ¹⁰⁰/₁₂₀ × 5880

= ^{100 × 5880}/₁₂₀

= ⁵⁸⁸⁰⁰⁰/₁₂₀

= 4900

Thus, Principal = $4900

Thus, the sum borrowed = $4900 Answer

Similar Questions

(1) Christopher took a loan of $6000 at the rate of 10% simple interest per annum. If he paid an amount of $11400 to clear the loan, then find the time period of the loan.

(2) Calculate the amount due after 9 years if Sarah borrowed a sum of $5850 at a rate of 3% simple interest.

(3) Susan had to pay $3978.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(4) What amount does Elizabeth have to pay after 6 years if he takes a loan of $3450 at 10% simple interest?

(5) Karen took a loan of $5900 at the rate of 8% simple interest per annum. If he paid an amount of $8732 to clear the loan, then find the time period of the loan.

(6) Calculate the amount due after 9 years if Christopher borrowed a sum of $6000 at a rate of 6% simple interest.

(7) Find the amount to be paid if Richard borrowed a sum of $5600 at 5% simple interest for 7 years.

(8) Barbara took a loan of $5100 at the rate of 6% simple interest per annum. If he paid an amount of $7548 to clear the loan, then find the time period of the loan.

(9) What amount does Joseph have to pay after 5 years if he takes a loan of $3700 at 8% simple interest?

(10) If Mary borrowed $3050 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.