Simple Interest
Math MCQs

Question :    If Sarah paid $4312 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

Correct Answer  $3850

Solution & Explanation

Solution

Given,

Amount (A) = $4312

Rate of Simple Interest (R) = 3%

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

$4312 = P (1 + 3% × 4)

⇒ $4312 = P (1 + ³/₁₀₀ × 4)

⇒ $4312 = P (1 + ^{3 × 4}/₁₀₀)

⇒ $4312 = P (1 + ¹²/₁₀₀)

⇒ $4312 = P (^{100 + 12}/₁₀₀)

⇒ $4312 = P × ¹¹²/₁₀₀

⇒ P × ¹¹²/₁₀₀ = $4312

⇒ P = ⁴³¹²/_¹¹²/100

⇒ P = 4312 × ¹⁰⁰/₁₁₂

⇒ P = ^{4312 × 100}/₁₁₂

⇒ P = ⁴³¹²⁰⁰/₁₁₂

⇒ P = $3850

Thus, the sum borrowed (P) = $3850 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 = 3% per annum

Thus, Interest = 3% of principal

⇒ Interest = 3% of 100 = 3

Thus, Simple Interest for 1 year = 3

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 × 3 = 12

Thus, simple interest for 4 years = 12

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 12 = 112

Calculation of the Principal

Now,

∵ If the Amount is 112, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₁₂

∴ If the Amount is 4312, then the Principal = ¹⁰⁰/₁₁₂ × 4312

= ^{100 × 4312}/₁₁₂

= ⁴³¹²⁰⁰/₁₁₂

= 3850

Thus, Principal = $3850

Thus, the sum borrowed = $3850 Answer

Similar Questions

(1) Calculate the amount due after 9 years if John borrowed a sum of $5200 at a rate of 5% simple interest.

(2) What amount will be due after 2 years if Mark borrowed a sum of $3700 at a 5% simple interest?

(3) Calculate the amount due after 9 years if Charles borrowed a sum of $5900 at a rate of 6% simple interest.

(4) Calculate the amount due after 9 years if Thomas borrowed a sum of $5800 at a rate of 8% simple interest.

(5) James had to pay $3360 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(6) If Ashley paid $4914 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(7) How much loan did Christopher borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7200 to clear it?

(8) What amount does Jennifer have to pay after 5 years if he takes a loan of $3250 at 5% simple interest?

(9) What amount does John have to pay after 6 years if he takes a loan of $3200 at 4% simple interest?

(10) Calculate the amount due if Patricia borrowed a sum of $3150 at 4% simple interest for 3 years.