Simple Interest
Math MCQs

Question :    Sarah had to pay $4312 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

Correct Answer  $3850

Solution & Explanation

Solution

Given,

Amount (A) = $4312

Rate of Simple Interest (R) = 4%

Time (T) = 3 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 + 4% × 3)

⇒ $4312 = P (1 + ⁴/₁₀₀ × 3)

⇒ $4312 = P (1 + ^{4 × 3}/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 = 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 = 3 years

So, we need to calculate the simple interest for the given time period, which is 3 years

Thus, Simple Interest for 3 years = 3 × Simple Interest for 1 year

= 3 × 4 = 12

Thus, simple interest for 3 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) Sarah took a loan of $5700 at the rate of 10% simple interest per annum. If he paid an amount of $9120 to clear the loan, then find the time period of the loan.

(2) Joseph took a loan of $5400 at the rate of 9% simple interest per annum. If he paid an amount of $9288 to clear the loan, then find the time period of the loan.

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

(4) Calculate the amount due if Jennifer borrowed a sum of $3250 at 10% simple interest for 3 years.

(5) Calculate the amount due after 9 years if Susan borrowed a sum of $5650 at a rate of 4% simple interest.

(6) David took a loan of $4800 at the rate of 7% simple interest per annum. If he paid an amount of $6816 to clear the loan, then find the time period of the loan.

(7) Richard took a loan of $5200 at the rate of 7% simple interest per annum. If he paid an amount of $8476 to clear the loan, then find the time period of the loan.

(8) What amount will be due after 2 years if Thomas borrowed a sum of $3400 at a 10% simple interest?

(9) What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 9% simple interest?

(10) Sarah took a loan of $5700 at the rate of 8% simple interest per annum. If he paid an amount of $9804 to clear the loan, then find the time period of the loan.