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) David took a loan of $4800 at the rate of 7% simple interest per annum. If he paid an amount of $7824 to clear the loan, then find the time period of the loan.

(2) If Steven paid $5520 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(3) What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 9% simple interest?

(4) Thomas took a loan of $5600 at the rate of 6% simple interest per annum. If he paid an amount of $8960 to clear the loan, then find the time period of the loan.

(5) Calculate the amount due if Sarah borrowed a sum of $3850 at 8% simple interest for 3 years.

(6) If Robert borrowed $3100 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.

(7) Calculate the amount due if Linda borrowed a sum of $3350 at 7% simple interest for 4 years.

(8) If Steven paid $5152 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(9) Robert took a loan of $4200 at the rate of 6% simple interest per annum. If he paid an amount of $6720 to clear the loan, then find the time period of the loan.

(10) How much loan did Paul borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8375 to clear it?