Simple Interest
Math MCQs

Question :    If Steven paid $5336 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

Correct Answer  $4600

Solution & Explanation

Solution

Given,

Amount (A) = $5336

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

$5336 = P (1 + 4% × 4)

⇒ $5336 = P (1 + ⁴/₁₀₀ × 4)

⇒ $5336 = P (1 + ^{4 × 4}/₁₀₀)

⇒ $5336 = P (1 + ¹⁶/₁₀₀)

⇒ $5336 = P (^{100 + 16}/₁₀₀)

⇒ $5336 = P × ¹¹⁶/₁₀₀

⇒ P × ¹¹⁶/₁₀₀ = $5336

⇒ P = ⁵³³⁶/_¹¹⁶/100

⇒ P = 5336 × ¹⁰⁰/₁₁₆

⇒ P = ^{5336 × 100}/₁₁₆

⇒ P = ⁵³³⁶⁰⁰/₁₁₆

⇒ P = $4600

Thus, the sum borrowed (P) = $4600 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 5336, then the Principal = ¹⁰⁰/₁₁₆ × 5336

= ^{100 × 5336}/₁₁₆

= ⁵³³⁶⁰⁰/₁₁₆

= 4600

Thus, Principal = $4600

Thus, the sum borrowed = $4600 Answer

Similar Questions

(1) Find the amount to be paid if Michael borrowed a sum of $5300 at 5% simple interest for 7 years.

(2) What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 4% simple interest?

(3) How much loan did Andrew borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8500 to clear it?

(4) Calculate the amount due if David borrowed a sum of $3400 at 7% simple interest for 3 years.

(5) If Karen paid $4266 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(6) If William paid $3920 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(7) If Karen paid $4582 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(8) How much loan did Barbara borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6382.5 to clear it?

(9) Calculate the amount due if Charles borrowed a sum of $3900 at 7% simple interest for 4 years.

(10) Find the amount to be paid if Karen borrowed a sum of $5950 at 9% simple interest for 7 years.