Simple Interest
Math MCQs

Question :    Barbara had to pay $3976 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  $3550

Solution & Explanation

Solution

Given,

Amount (A) = $3976

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

$3976 = P (1 + 4% × 3)

⇒ $3976 = P (1 + ⁴/₁₀₀ × 3)

⇒ $3976 = P (1 + ^{4 × 3}/₁₀₀)

⇒ $3976 = P (1 + ¹²/₁₀₀)

⇒ $3976 = P (^{100 + 12}/₁₀₀)

⇒ $3976 = P × ¹¹²/₁₀₀

⇒ P × ¹¹²/₁₀₀ = $3976

⇒ P = ³⁹⁷⁶/_¹¹²/100

⇒ P = 3976 × ¹⁰⁰/₁₁₂

⇒ P = ^{3976 × 100}/₁₁₂

⇒ P = ³⁹⁷⁶⁰⁰/₁₁₂

⇒ P = $3550

Thus, the sum borrowed (P) = $3550 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 3976, then the Principal = ¹⁰⁰/₁₁₂ × 3976

= ^{100 × 3976}/₁₁₂

= ³⁹⁷⁶⁰⁰/₁₁₂

= 3550

Thus, Principal = $3550

Thus, the sum borrowed = $3550 Answer

Similar Questions

(1) Anthony took a loan of $6600 at the rate of 7% simple interest per annum. If he paid an amount of $9834 to clear the loan, then find the time period of the loan.

(2) What amount does Patricia have to pay after 5 years if he takes a loan of $3150 at 10% simple interest?

(3) Calculate the amount due if Mary borrowed a sum of $3050 at 4% simple interest for 3 years.

(4) Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 5% simple interest.

(5) Calculate the amount due if John borrowed a sum of $3200 at 2% simple interest for 4 years.

(6) Michelle had to pay $5247 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(7) David took a loan of $4800 at the rate of 8% simple interest per annum. If he paid an amount of $7872 to clear the loan, then find the time period of the loan.

(8) Richard took a loan of $5200 at the rate of 7% simple interest per annum. If he paid an amount of $7384 to clear the loan, then find the time period of the loan.

(9) Lisa took a loan of $6100 at the rate of 10% simple interest per annum. If he paid an amount of $10370 to clear the loan, then find the time period of the loan.

(10) Calculate the amount due if William borrowed a sum of $3500 at 8% simple interest for 4 years.