Simple Interest
Math MCQs

Question :    If Barbara paid $4118 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

Correct Answer  $3550

Solution & Explanation

Solution

Given,

Amount (A) = $4118

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

$4118 = P (1 + 4% × 4)

⇒ $4118 = P (1 + ⁴/₁₀₀ × 4)

⇒ $4118 = P (1 + ^{4 × 4}/₁₀₀)

⇒ $4118 = P (1 + ¹⁶/₁₀₀)

⇒ $4118 = P (^{100 + 16}/₁₀₀)

⇒ $4118 = P × ¹¹⁶/₁₀₀

⇒ P × ¹¹⁶/₁₀₀ = $4118

⇒ P = ⁴¹¹⁸/_¹¹⁶/100

⇒ P = 4118 × ¹⁰⁰/₁₁₆

⇒ P = ^{4118 × 100}/₁₁₆

⇒ P = ⁴¹¹⁸⁰⁰/₁₁₆

⇒ P = $3550

Thus, the sum borrowed (P) = $3550 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 4118, then the Principal = ¹⁰⁰/₁₁₆ × 4118

= ^{100 × 4118}/₁₁₆

= ⁴¹¹⁸⁰⁰/₁₁₆

= 3550

Thus, Principal = $3550

Thus, the sum borrowed = $3550 Answer

Similar Questions

(1) What amount does Linda have to pay after 6 years if he takes a loan of $3350 at 4% simple interest?

(2) Calculate the amount due if Richard borrowed a sum of $3600 at 7% simple interest for 4 years.

(3) If Ashley paid $5460 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(4) Find the amount to be paid if James borrowed a sum of $5000 at 7% simple interest for 7 years.

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

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

(7) 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.

(8) Linda took a loan of $4700 at the rate of 9% simple interest per annum. If he paid an amount of $7238 to clear the loan, then find the time period of the loan.

(9) Andrew had to pay $5520 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(10) How much loan did Joshua borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8280 to clear it?