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) Daniel took a loan of $6200 at the rate of 6% simple interest per annum. If he paid an amount of $8804 to clear the loan, then find the time period of the loan.

(2) In how much time a principal of $3050 will amount to $3355 at a simple interest of 5% per annum?

(3) Elizabeth had to pay $3657 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 Nancy borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7687.5 to clear it?

(5) What amount does Karen have to pay after 5 years if he takes a loan of $3950 at 8% simple interest?

(6) Calculate the amount due if Jessica borrowed a sum of $3750 at 6% simple interest for 3 years.

(7) Find the amount to be paid if Mary borrowed a sum of $5050 at 5% simple interest for 8 years.

(8) Find the amount to be paid if Joseph borrowed a sum of $5700 at 10% simple interest for 7 years.

(9) What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 6% simple interest?

(10) Calculate the amount due after 10 years if John borrowed a sum of $5200 at a rate of 4% simple interest.