Simple Interest
Math MCQs

Question :    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.

Correct Answer  $3950

Solution & Explanation

Solution

Given,

Amount (A) = $4187

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

$4187 = P (1 + 2% × 3)

⇒ $4187 = P (1 + ²/₁₀₀ × 3)

⇒ $4187 = P (1 + ^{2 × 3}/₁₀₀)

⇒ $4187 = P (1 + ⁶/₁₀₀)

⇒ $4187 = P (^{100 + 6}/₁₀₀)

⇒ $4187 = P × ¹⁰⁶/₁₀₀

⇒ P × ¹⁰⁶/₁₀₀ = $4187

⇒ P = ⁴¹⁸⁷/_¹⁰⁶/100

⇒ P = 4187 × ¹⁰⁰/₁₀₆

⇒ P = ^{4187 × 100}/₁₀₆

⇒ P = ⁴¹⁸⁷⁰⁰/₁₀₆

⇒ P = $3950

Thus, the sum borrowed (P) = $3950 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 4187, then the Principal = ¹⁰⁰/₁₀₆ × 4187

= ^{100 × 4187}/₁₀₆

= ⁴¹⁸⁷⁰⁰/₁₀₆

= 3950

Thus, Principal = $3950

Thus, the sum borrowed = $3950 Answer

Similar Questions

(1) Find the amount to be paid if Patricia borrowed a sum of $5150 at 10% simple interest for 8 years.

(2) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 3% simple interest for 8 years.

(3) Barbara took a loan of $5100 at the rate of 6% simple interest per annum. If he paid an amount of $8160 to clear the loan, then find the time period of the loan.

(4) How much loan did Joshua borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7590 to clear it?

(5) What amount does Barbara have to pay after 6 years if he takes a loan of $3550 at 9% simple interest?

(6) How much loan did Anthony borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6930 to clear it?

(7) What amount will be due after 2 years if Paul borrowed a sum of $3850 at a 8% simple interest?

(8) Calculate the amount due after 9 years if Barbara borrowed a sum of $5550 at a rate of 8% simple interest.

(9) How much loan did Michelle borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8687.5 to clear it?

(10) If Karen paid $4266 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.