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) Calculate the amount due if Mary borrowed a sum of $3050 at 5% simple interest for 4 years.

(2) What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 4% simple interest?

(3) Christopher had to pay $4600 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(4) If Matthew paid $5040 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(5) If Donald paid $5040 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(6) What amount does Jessica have to pay after 5 years if he takes a loan of $3750 at 5% simple interest?

(7) Calculate the amount due after 9 years if Susan borrowed a sum of $5650 at a rate of 7% simple interest.

(8) What amount does Richard have to pay after 5 years if he takes a loan of $3600 at 9% simple interest?

(9) 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?

(10) What amount does Patricia have to pay after 6 years if he takes a loan of $3150 at 7% simple interest?