Simple Interest
Math MCQs

Question :    Richard had to pay $3816 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

Correct Answer  $3600

Solution & Explanation

Solution

Given,

Amount (A) = $3816

Rate of Simple Interest (R) = 2%

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

$3816 = P (1 + 2% × 3)

⇒ $3816 = P (1 + ²/₁₀₀ × 3)

⇒ $3816 = P (1 + ^{2 × 3}/₁₀₀)

⇒ $3816 = P (1 + ⁶/₁₀₀)

⇒ $3816 = P (^{100 + 6}/₁₀₀)

⇒ $3816 = P × ¹⁰⁶/₁₀₀

⇒ P × ¹⁰⁶/₁₀₀ = $3816

⇒ P = ³⁸¹⁶/_¹⁰⁶/100

⇒ P = 3816 × ¹⁰⁰/₁₀₆

⇒ P = ^{3816 × 100}/₁₀₆

⇒ P = ³⁸¹⁶⁰⁰/₁₀₆

⇒ P = $3600

Thus, the sum borrowed (P) = $3600 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 = 2% per annum

Thus, Interest = 2% of principal

⇒ Interest = 2% of 100 = 2

Thus, Simple Interest for 1 year = 2

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 × 2 = 6

Thus, simple interest for 3 years = 6

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 6 = 106

Calculation of the Principal

Now,

∵ If the Amount is 106, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₀₆

∴ If the Amount is 3816, then the Principal = ¹⁰⁰/₁₀₆ × 3816

= ^{100 × 3816}/₁₀₆

= ³⁸¹⁶⁰⁰/₁₀₆

= 3600

Thus, Principal = $3600

Thus, the sum borrowed = $3600 Answer

Similar Questions

(1) If Kenneth paid $5600 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(2) Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 3% simple interest.

(3) What amount does Richard have to pay after 5 years if he takes a loan of $3600 at 9% simple interest?

(4) Calculate the amount due after 9 years if Jennifer borrowed a sum of $5250 at a rate of 4% simple interest.

(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 Christopher borrowed a sum of $6000 at 4% simple interest for 7 years.

(7) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 3% simple interest?

(8) How much loan did Edward borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8740 to clear it?

(9) How much loan did Christopher borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6600 to clear it?

(10) Calculate the amount due after 9 years if Elizabeth borrowed a sum of $5450 at a rate of 7% simple interest.