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) Charles took a loan of $5800 at the rate of 9% simple interest per annum. If he paid an amount of $9976 to clear the loan, then find the time period of the loan.

(2) Margaret took a loan of $6700 at the rate of 10% simple interest per annum. If he paid an amount of $10720 to clear the loan, then find the time period of the loan.

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

(4) How much loan did Deborah borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8195 to clear it?

(5) 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.

(6) Calculate the amount due if Joseph borrowed a sum of $3700 at 8% simple interest for 4 years.

(7) Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 5% simple interest.

(8) Charles had to pay $4251 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(9) Find the amount to be paid if Sarah borrowed a sum of $5850 at 5% simple interest for 7 years.

(10) In how much time a principal of $3150 will amount to $3339 at a simple interest of 3% per annum?