Simple Interest
Math MCQs

Question :    William had to pay $3920 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

Correct Answer  $3500

Solution & Explanation

Solution

Given,

Amount (A) = $3920

Rate of Simple Interest (R) = 4%

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

$3920 = P (1 + 4% × 3)

⇒ $3920 = P (1 + ⁴/₁₀₀ × 3)

⇒ $3920 = P (1 + ^{4 × 3}/₁₀₀)

⇒ $3920 = P (1 + ¹²/₁₀₀)

⇒ $3920 = P (^{100 + 12}/₁₀₀)

⇒ $3920 = P × ¹¹²/₁₀₀

⇒ P × ¹¹²/₁₀₀ = $3920

⇒ P = ³⁹²⁰/_¹¹²/100

⇒ P = 3920 × ¹⁰⁰/₁₁₂

⇒ P = ^{3920 × 100}/₁₁₂

⇒ P = ³⁹²⁰⁰⁰/₁₁₂

⇒ P = $3500

Thus, the sum borrowed (P) = $3500 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 = 4% per annum

Thus, Interest = 4% of principal

⇒ Interest = 4% of 100 = 4

Thus, Simple Interest for 1 year = 4

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 × 4 = 12

Thus, simple interest for 3 years = 12

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 12 = 112

Calculation of the Principal

Now,

∵ If the Amount is 112, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₁₂

∴ If the Amount is 3920, then the Principal = ¹⁰⁰/₁₁₂ × 3920

= ^{100 × 3920}/₁₁₂

= ³⁹²⁰⁰⁰/₁₁₂

= 3500

Thus, Principal = $3500

Thus, the sum borrowed = $3500 Answer

Similar Questions

(1) How much loan did David borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6480 to clear it?

(2) Calculate the amount due if Charles borrowed a sum of $3900 at 2% simple interest for 4 years.

(3) Calculate the amount due after 9 years if Susan borrowed a sum of $5650 at a rate of 8% simple interest.

(4) Find the amount to be paid if Karen borrowed a sum of $5950 at 10% simple interest for 7 years.

(5) If Charles paid $4368 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(6) Find the amount to be paid if John borrowed a sum of $5200 at 6% simple interest for 8 years.

(7) Richard took a loan of $5200 at the rate of 6% simple interest per annum. If he paid an amount of $7384 to clear the loan, then find the time period of the loan.

(8) Jennifer took a loan of $4500 at the rate of 6% simple interest per annum. If he paid an amount of $6120 to clear the loan, then find the time period of the loan.

(9) Michelle had to pay $5247 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(10) What amount does James have to pay after 5 years if he takes a loan of $3000 at 2% simple interest?