Simple Interest
Math MCQs

Question :    Margaret had to pay $4611 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  $4350

Solution & Explanation

Solution

Given,

Amount (A) = $4611

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

$4611 = P (1 + 2% × 3)

⇒ $4611 = P (1 + ²/₁₀₀ × 3)

⇒ $4611 = P (1 + ^{2 × 3}/₁₀₀)

⇒ $4611 = P (1 + ⁶/₁₀₀)

⇒ $4611 = P (^{100 + 6}/₁₀₀)

⇒ $4611 = P × ¹⁰⁶/₁₀₀

⇒ P × ¹⁰⁶/₁₀₀ = $4611

⇒ P = ⁴⁶¹¹/_¹⁰⁶/100

⇒ P = 4611 × ¹⁰⁰/₁₀₆

⇒ P = ^{4611 × 100}/₁₀₆

⇒ P = ⁴⁶¹¹⁰⁰/₁₀₆

⇒ P = $4350

Thus, the sum borrowed (P) = $4350 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 4611, then the Principal = ¹⁰⁰/₁₀₆ × 4611

= ^{100 × 4611}/₁₀₆

= ⁴⁶¹¹⁰⁰/₁₀₆

= 4350

Thus, Principal = $4350

Thus, the sum borrowed = $4350 Answer

Similar Questions

(1) In how much time a principal of $3050 will amount to $3416 at a simple interest of 3% per annum?

(2) What amount does David have to pay after 5 years if he takes a loan of $3400 at 4% simple interest?

(3) What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 3% simple interest?

(4) Calculate the amount due after 10 years if Joseph borrowed a sum of $5700 at a rate of 10% simple interest.

(5) Calculate the amount due after 9 years if Barbara borrowed a sum of $5550 at a rate of 7% simple interest.

(6) What amount does Thomas have to pay after 6 years if he takes a loan of $3800 at 5% simple interest?

(7) If David paid $3672 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(8) What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 10% simple interest?

(9) What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 2% simple interest?

(10) Betty took a loan of $6500 at the rate of 6% simple interest per annum. If he paid an amount of $10010 to clear the loan, then find the time period of the loan.