Simple Interest
Math MCQs

Question :    If John paid $3840 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

Correct Answer  $3200

Solution & Explanation

Solution

Given,

Amount (A) = $3840

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

$3840 = P (1 + 5% × 4)

⇒ $3840 = P (1 + ⁵/₁₀₀ × 4)

⇒ $3840 = P (1 + ^{5 × 4}/₁₀₀)

⇒ $3840 = P (1 + ²⁰/₁₀₀)

⇒ $3840 = P (^{100 + 20}/₁₀₀)

⇒ $3840 = P × ¹²⁰/₁₀₀

⇒ P × ¹²⁰/₁₀₀ = $3840

⇒ P = ³⁸⁴⁰/_¹²⁰/100

⇒ P = 3840 × ¹⁰⁰/₁₂₀

⇒ P = ^{3840 × 100}/₁₂₀

⇒ P = ³⁸⁴⁰⁰⁰/₁₂₀

⇒ P = $3200

Thus, the sum borrowed (P) = $3200 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 3840, then the Principal = ¹⁰⁰/₁₂₀ × 3840

= ^{100 × 3840}/₁₂₀

= ³⁸⁴⁰⁰⁰/₁₂₀

= 3200

Thus, Principal = $3200

Thus, the sum borrowed = $3200 Answer

Similar Questions

(1) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 9% simple interest?

(2) What amount does Richard have to pay after 5 years if he takes a loan of $3600 at 8% simple interest?

(3) What amount does Michael have to pay after 5 years if he takes a loan of $3300 at 10% simple interest?

(4) In how much time a principal of $3150 will amount to $3465 at a simple interest of 5% per annum?

(5) Find the amount to be paid if John borrowed a sum of $5200 at 8% simple interest for 7 years.

(6) Patricia took a loan of $4300 at the rate of 10% simple interest per annum. If he paid an amount of $6880 to clear the loan, then find the time period of the loan.

(7) John took a loan of $4400 at the rate of 7% simple interest per annum. If he paid an amount of $7172 to clear the loan, then find the time period of the loan.

(8) 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.

(9) Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 9% simple interest.

(10) In how much time a principal of $3000 will amount to $3240 at a simple interest of 2% per annum?