Simple Interest
Math MCQs

Question :  ( 1 of 10 )  If Barbara paid $3976 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

Correct Answer  $3550

Solution & Explanation

Solution

Given,

Amount (A) = $3976

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

$3976 = P (1 + 3% × 4)

⇒ $3976 = P (1 + ³/₁₀₀ × 4)

⇒ $3976 = P (1 + ^{3 × 4}/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 = 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 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) Find the amount to be paid if Susan borrowed a sum of $5650 at 7% simple interest for 8 years.

(2) How much loan did Mark borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7040 to clear it?

(3) In how much time a principal of $3150 will amount to $3402 at a simple interest of 4% per annum?

(4) Charles took a loan of $5800 at the rate of 7% simple interest per annum. If he paid an amount of $9048 to clear the loan, then find the time period of the loan.

(5) Christopher took a loan of $6000 at the rate of 7% simple interest per annum. If he paid an amount of $8520 to clear the loan, then find the time period of the loan.

(6) What amount does James have to pay after 5 years if he takes a loan of $3000 at 7% simple interest?

(7) What amount does Joseph have to pay after 5 years if he takes a loan of $3700 at 4% simple interest?

(8) Calculate the amount due after 9 years if Elizabeth borrowed a sum of $5450 at a rate of 4% simple interest.

(9) Calculate the amount due if Mary borrowed a sum of $3050 at 5% simple interest for 3 years.

(10) Calculate the amount due if Christopher borrowed a sum of $4000 at 5% simple interest for 4 years.