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) Sandra took a loan of $6900 at the rate of 8% simple interest per annum. If he paid an amount of $10212 to clear the loan, then find the time period of the loan.

(2) If Susan paid $4088 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(3) Karen had to pay $4187 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(4) How much loan did Kenneth borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8400 to clear it?

(5) Find the amount to be paid if Christopher borrowed a sum of $6000 at 3% simple interest for 8 years.

(6) Find the amount to be paid if Linda borrowed a sum of $5350 at 2% simple interest for 8 years.

(7) Calculate the amount due after 9 years if Jessica borrowed a sum of $5750 at a rate of 2% simple interest.

(8) Calculate the amount due if Charles borrowed a sum of $3900 at 5% simple interest for 4 years.

(9) What amount does Joseph have to pay after 5 years if he takes a loan of $3700 at 3% simple interest?

(10) What amount does Michael have to pay after 5 years if he takes a loan of $3300 at 8% simple interest?