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) What amount will be due after 2 years if Thomas borrowed a sum of $3400 at a 10% simple interest?

(2) Jessica took a loan of $5500 at the rate of 10% simple interest per annum. If he paid an amount of $10450 to clear the loan, then find the time period of the loan.

(3) Matthew took a loan of $6400 at the rate of 10% simple interest per annum. If he paid an amount of $11520 to clear the loan, then find the time period of the loan.

(4) Michael had to pay $3597 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(5) Mary took a loan of $4100 at the rate of 10% simple interest per annum. If he paid an amount of $6970 to clear the loan, then find the time period of the loan.

(6) How much loan did Sharon borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9300 to clear it?

(7) How much loan did Daniel borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7015 to clear it?

(8) How much loan did Carol borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8107.5 to clear it?

(9) What amount does Mary have to pay after 5 years if he takes a loan of $3050 at 10% simple interest?

(10) Thomas took a loan of $5600 at the rate of 8% simple interest per annum. If he paid an amount of $10080 to clear the loan, then find the time period of the loan.