Simple Interest
Math MCQs

Question :    How much loan did William borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6600 to clear it?

Correct Answer  $5500

Solution & Explanation

Solution

Given,

Amount (A) = $6600

Rate of Simple Interest (R) = 4%

Time (T) = 5 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

$6600 = P (1 + 4% × 5)

⇒ $6600 = P (1 + ⁴/₁₀₀ × 5)

⇒ $6600 = P (1 + ^{4 × 5}/₁₀₀)

⇒ $6600 = P (1 + ²⁰/₁₀₀)

⇒ $6600 = P (^{100 + 20}/₁₀₀)

⇒ $6600 = P × ¹²⁰/₁₀₀

⇒ P × ¹²⁰/₁₀₀ = $6600

⇒ P = ⁶⁶⁰⁰/_¹²⁰/100

⇒ P = 6600 × ¹⁰⁰/₁₂₀

⇒ P = ^{6600 × 100}/₁₂₀

⇒ P = ⁶⁶⁰⁰⁰⁰/₁₂₀

⇒ P = $5500

Thus, the sum borrowed (P) = $5500 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 = 5 years

So, we need to calculate the simple interest for the given time period, which is 5 years

Thus, Simple Interest for 5 years = 5 × Simple Interest for 1 year

= 5 × 4 = 20

Thus, simple interest for 5 years = 20

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 20 = 120

Calculation of the Principal

Now,

∵ If the Amount is 120, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₂₀

∴ If the Amount is 6600, then the Principal = ¹⁰⁰/₁₂₀ × 6600

= ^{100 × 6600}/₁₂₀

= ⁶⁶⁰⁰⁰⁰/₁₂₀

= 5500

Thus, Principal = $5500

Thus, the sum borrowed = $5500 Answer

Similar Questions

(1) Calculate the amount due if Thomas borrowed a sum of $3800 at 8% simple interest for 4 years.

(2) What amount does Mary have to pay after 5 years if he takes a loan of $3050 at 6% simple interest?

(3) How much loan did Timothy borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9250 to clear it?

(4) If William paid $3780 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(5) Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 8% simple interest.

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

(7) How much loan did Robert borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6120 to clear it?

(8) How much loan did Donald borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7800 to clear it?

(9) What amount does Patricia have to pay after 6 years if he takes a loan of $3150 at 2% simple interest?

(10) Karen took a loan of $5900 at the rate of 10% simple interest per annum. If he paid an amount of $11800 to clear the loan, then find the time period of the loan.