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) Sarah took a loan of $5700 at the rate of 10% simple interest per annum. If he paid an amount of $10260 to clear the loan, then find the time period of the loan.

(2) Donna had to pay $5432 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(3) What amount does Michael have to pay after 5 years if he takes a loan of $3300 at 10% simple interest?

(4) Elizabeth took a loan of $4900 at the rate of 7% simple interest per annum. If he paid an amount of $6958 to clear the loan, then find the time period of the loan.

(5) Calculate the amount due if Richard borrowed a sum of $3600 at 4% simple interest for 4 years.

(6) Mary took a loan of $4100 at the rate of 10% simple interest per annum. If he paid an amount of $7790 to clear the loan, then find the time period of the loan.

(7) Jessica took a loan of $5500 at the rate of 9% simple interest per annum. If he paid an amount of $9460 to clear the loan, then find the time period of the loan.

(8) Calculate the amount due after 10 years if John borrowed a sum of $5200 at a rate of 3% simple interest.

(9) Linda took a loan of $4700 at the rate of 8% simple interest per annum. If he paid an amount of $7708 to clear the loan, then find the time period of the loan.

(10) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 10% simple interest?