Simple Interest
Math MCQs

Question :    Paul had to pay $4982 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  $4700

Solution & Explanation

Solution

Given,

Amount (A) = $4982

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

$4982 = P (1 + 2% × 3)

⇒ $4982 = P (1 + ²/₁₀₀ × 3)

⇒ $4982 = P (1 + ^{2 × 3}/₁₀₀)

⇒ $4982 = P (1 + ⁶/₁₀₀)

⇒ $4982 = P (^{100 + 6}/₁₀₀)

⇒ $4982 = P × ¹⁰⁶/₁₀₀

⇒ P × ¹⁰⁶/₁₀₀ = $4982

⇒ P = ⁴⁹⁸²/_¹⁰⁶/100

⇒ P = 4982 × ¹⁰⁰/₁₀₆

⇒ P = ^{4982 × 100}/₁₀₆

⇒ P = ⁴⁹⁸²⁰⁰/₁₀₆

⇒ P = $4700

Thus, the sum borrowed (P) = $4700 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 4982, then the Principal = ¹⁰⁰/₁₀₆ × 4982

= ^{100 × 4982}/₁₀₆

= ⁴⁹⁸²⁰⁰/₁₀₆

= 4700

Thus, Principal = $4700

Thus, the sum borrowed = $4700 Answer

Similar Questions

(1) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 3% simple interest?

(2) Lisa took a loan of $6100 at the rate of 7% simple interest per annum. If he paid an amount of $9943 to clear the loan, then find the time period of the loan.

(3) What amount will be due after 2 years if Joshua borrowed a sum of $3950 at a 6% simple interest?

(4) Paul had to pay $4982 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(5) Calculate the amount due after 9 years if Michael borrowed a sum of $5300 at a rate of 5% simple interest.

(6) Calculate the amount due if Sarah borrowed a sum of $3850 at 10% simple interest for 3 years.

(7) Calculate the amount due after 10 years if Joseph borrowed a sum of $5700 at a rate of 3% simple interest.

(8) What amount does Jessica have to pay after 5 years if he takes a loan of $3750 at 8% simple interest?

(9) Linda took a loan of $4700 at the rate of 10% simple interest per annum. If he paid an amount of $9400 to clear the loan, then find the time period of the loan.

(10) Calculate the amount due if Christopher borrowed a sum of $4000 at 7% simple interest for 3 years.