Simple Interest
Math MCQs

Question :    If Richard paid $4176 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

Correct Answer  $3600

Solution & Explanation

Solution

Given,

Amount (A) = $4176

Rate of Simple Interest (R) = 4%

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

$4176 = P (1 + 4% × 4)

⇒ $4176 = P (1 + ⁴/₁₀₀ × 4)

⇒ $4176 = P (1 + ^{4 × 4}/₁₀₀)

⇒ $4176 = P (1 + ¹⁶/₁₀₀)

⇒ $4176 = P (^{100 + 16}/₁₀₀)

⇒ $4176 = P × ¹¹⁶/₁₀₀

⇒ P × ¹¹⁶/₁₀₀ = $4176

⇒ P = ⁴¹⁷⁶/_¹¹⁶/100

⇒ P = 4176 × ¹⁰⁰/₁₁₆

⇒ P = ^{4176 × 100}/₁₁₆

⇒ P = ⁴¹⁷⁶⁰⁰/₁₁₆

⇒ P = $3600

Thus, the sum borrowed (P) = $3600 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 = 4% per annum

Thus, Interest = 4% of principal

⇒ Interest = 4% of 100 = 4

Thus, Simple Interest for 1 year = 4

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 × 4 = 16

Thus, simple interest for 4 years = 16

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 16 = 116

Calculation of the Principal

Now,

∵ If the Amount is 116, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₁₆

∴ If the Amount is 4176, then the Principal = ¹⁰⁰/₁₁₆ × 4176

= ^{100 × 4176}/₁₁₆

= ⁴¹⁷⁶⁰⁰/₁₁₆

= 3600

Thus, Principal = $3600

Thus, the sum borrowed = $3600 Answer

Similar Questions

(1) Calculate the amount due after 9 years if Linda borrowed a sum of $5350 at a rate of 10% simple interest.

(2) Sarah took a loan of $5700 at the rate of 7% simple interest per annum. If he paid an amount of $9690 to clear the loan, then find the time period of the loan.

(3) Find the amount to be paid if Joseph borrowed a sum of $5700 at 8% simple interest for 7 years.

(4) Find the amount to be paid if Linda borrowed a sum of $5350 at 3% simple interest for 8 years.

(5) If James paid $3360 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(6) Calculate the amount due after 9 years if Richard borrowed a sum of $5600 at a rate of 6% simple interest.

(7) Calculate the amount due if Mary borrowed a sum of $3050 at 3% simple interest for 4 years.

(8) If Christopher borrowed $4000 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 Robert have to pay after 5 years if he takes a loan of $3100 at 3% simple interest?

(10) How much loan did Matthew borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7440 to clear it?