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) How much loan did Charles borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7080 to clear it?

(2) Find the amount to be paid if Charles borrowed a sum of $5900 at 2% simple interest for 8 years.

(3) How much loan did Joseph borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6555 to clear it?

(4) What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 6% simple interest?

(5) What amount does John have to pay after 6 years if he takes a loan of $3200 at 7% simple interest?

(6) What amount will be due after 2 years if Steven borrowed a sum of $3800 at a 6% simple interest?

(7) Calculate the amount due if Susan borrowed a sum of $3650 at 2% simple interest for 3 years.

(8) If Elizabeth borrowed $3450 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.

(9) What amount does Mary have to pay after 5 years if he takes a loan of $3050 at 7% simple interest?

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