Simple Interest
Math MCQs

Question :    Charles had to pay $4251 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

Correct Answer  $3900

Solution & Explanation

Solution

Given,

Amount (A) = $4251

Rate of Simple Interest (R) = 3%

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

$4251 = P (1 + 3% × 3)

⇒ $4251 = P (1 + ³/₁₀₀ × 3)

⇒ $4251 = P (1 + ^{3 × 3}/₁₀₀)

⇒ $4251 = P (1 + ⁹/₁₀₀)

⇒ $4251 = P (^{100 + 9}/₁₀₀)

⇒ $4251 = P × ¹⁰⁹/₁₀₀

⇒ P × ¹⁰⁹/₁₀₀ = $4251

⇒ P = ⁴²⁵¹/_¹⁰⁹/100

⇒ P = 4251 × ¹⁰⁰/₁₀₉

⇒ P = ^{4251 × 100}/₁₀₉

⇒ P = ⁴²⁵¹⁰⁰/₁₀₉

⇒ P = $3900

Thus, the sum borrowed (P) = $3900 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 = 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 × 3 = 9

Thus, simple interest for 3 years = 9

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 9 = 109

Calculation of the Principal

Now,

∵ If the Amount is 109, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₀₉

∴ If the Amount is 4251, then the Principal = ¹⁰⁰/₁₀₉ × 4251

= ^{100 × 4251}/₁₀₉

= ⁴²⁵¹⁰⁰/₁₀₉

= 3900

Thus, Principal = $3900

Thus, the sum borrowed = $3900 Answer

Similar Questions

(1) Sandra took a loan of $6900 at the rate of 7% simple interest per annum. If he paid an amount of $10764 to clear the loan, then find the time period of the loan.

(2) Robert took a loan of $4200 at the rate of 7% simple interest per annum. If he paid an amount of $5964 to clear the loan, then find the time period of the loan.

(3) Christopher took a loan of $6000 at the rate of 10% simple interest per annum. If he paid an amount of $12000 to clear the loan, then find the time period of the loan.

(4) What amount does Richard have to pay after 5 years if he takes a loan of $3600 at 6% simple interest?

(5) Find the amount to be paid if Susan borrowed a sum of $5650 at 9% simple interest for 8 years.

(6) How much loan did Cynthia borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8745 to clear it?

(7) Mary had to pay $3507.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(8) Calculate the amount due if Robert borrowed a sum of $3100 at 2% simple interest for 3 years.

(9) Matthew took a loan of $6400 at the rate of 9% simple interest per annum. If he paid an amount of $10432 to clear the loan, then find the time period of the loan.

(10) Find the amount to be paid if Thomas borrowed a sum of $5800 at 8% simple interest for 7 years.