Simple Interest
Math MCQs

Question :    If Margaret paid $5220 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

Correct Answer  $4350

Solution & Explanation

Solution

Given,

Amount (A) = $5220

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

$5220 = P (1 + 5% × 4)

⇒ $5220 = P (1 + ⁵/₁₀₀ × 4)

⇒ $5220 = P (1 + ^{5 × 4}/₁₀₀)

⇒ $5220 = P (1 + ²⁰/₁₀₀)

⇒ $5220 = P (^{100 + 20}/₁₀₀)

⇒ $5220 = P × ¹²⁰/₁₀₀

⇒ P × ¹²⁰/₁₀₀ = $5220

⇒ P = ⁵²²⁰/_¹²⁰/100

⇒ P = 5220 × ¹⁰⁰/₁₂₀

⇒ P = ^{5220 × 100}/₁₂₀

⇒ P = ⁵²²⁰⁰⁰/₁₂₀

⇒ P = $4350

Thus, the sum borrowed (P) = $4350 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 5220, then the Principal = ¹⁰⁰/₁₂₀ × 5220

= ^{100 × 5220}/₁₂₀

= ⁵²²⁰⁰⁰/₁₂₀

= 4350

Thus, Principal = $4350

Thus, the sum borrowed = $4350 Answer

Similar Questions

(1) Calculate the amount due after 10 years if Thomas borrowed a sum of $5800 at a rate of 10% simple interest.

(2) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 5% simple interest?

(3) If Andrew paid $5376 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(4) Michael took a loan of $4600 at the rate of 8% simple interest per annum. If he paid an amount of $7912 to clear the loan, then find the time period of the loan.

(5) Donald had to pay $4770 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(6) What amount does Michael have to pay after 5 years if he takes a loan of $3300 at 7% simple interest?

(7) Find the amount to be paid if Barbara borrowed a sum of $5550 at 6% simple interest for 8 years.

(8) Calculate the amount due after 10 years if Charles borrowed a sum of $5900 at a rate of 3% simple interest.

(9) How much loan did Jacob borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9600 to clear it?

(10) Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 8% simple interest.