Simple Interest
Math MCQs

Question :    If William paid $4200 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

Correct Answer  $3500

Solution & Explanation

Solution

Given,

Amount (A) = $4200

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

$4200 = P (1 + 5% × 4)

⇒ $4200 = P (1 + ⁵/₁₀₀ × 4)

⇒ $4200 = P (1 + ^{5 × 4}/₁₀₀)

⇒ $4200 = P (1 + ²⁰/₁₀₀)

⇒ $4200 = P (^{100 + 20}/₁₀₀)

⇒ $4200 = P × ¹²⁰/₁₀₀

⇒ P × ¹²⁰/₁₀₀ = $4200

⇒ P = ⁴²⁰⁰/_¹²⁰/100

⇒ P = 4200 × ¹⁰⁰/₁₂₀

⇒ P = ^{4200 × 100}/₁₂₀

⇒ P = ⁴²⁰⁰⁰⁰/₁₂₀

⇒ P = $3500

Thus, the sum borrowed (P) = $3500 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 4200, then the Principal = ¹⁰⁰/₁₂₀ × 4200

= ^{100 × 4200}/₁₂₀

= ⁴²⁰⁰⁰⁰/₁₂₀

= 3500

Thus, Principal = $3500

Thus, the sum borrowed = $3500 Answer

Similar Questions

(1) Find the amount to be paid if Charles borrowed a sum of $5900 at 5% simple interest for 8 years.

(2) Calculate the amount due if Barbara borrowed a sum of $3550 at 9% simple interest for 3 years.

(3) Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 10% simple interest.

(4) Calculate the amount due if Karen borrowed a sum of $3950 at 10% simple interest for 3 years.

(5) What amount will be due after 2 years if William borrowed a sum of $3250 at a 7% simple interest?

(6) How much loan did Carol borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8460 to clear it?

(7) If Donald paid $5220 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(8) Sandra took a loan of $6900 at the rate of 6% simple interest per annum. If he paid an amount of $9384 to clear the loan, then find the time period of the loan.

(9) Calculate the amount due if William borrowed a sum of $3500 at 3% simple interest for 3 years.

(10) Lisa took a loan of $6100 at the rate of 9% simple interest per annum. If he paid an amount of $10492 to clear the loan, then find the time period of the loan.