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) Michael took a loan of $4600 at the rate of 8% simple interest per annum. If he paid an amount of $6808 to clear the loan, then find the time period of the loan.

(2) What amount will be due after 2 years if Anthony borrowed a sum of $3650 at a 9% simple interest?

(3) Calculate the amount due if Jennifer borrowed a sum of $3250 at 4% simple interest for 4 years.

(4) Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 6% simple interest.

(5) Susan took a loan of $5300 at the rate of 10% simple interest per annum. If he paid an amount of $10600 to clear the loan, then find the time period of the loan.

(6) What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 9% simple interest?

(7) Calculate the amount due after 10 years if Jennifer borrowed a sum of $5250 at a rate of 3% simple interest.

(8) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 6% simple interest for 3 years.

(9) How much loan did Susan borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6215 to clear it?

(10) Find the amount to be paid if Linda borrowed a sum of $5350 at 5% simple interest for 8 years.