Simple Interest
Math MCQs

Question :    If William paid $4060 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

Correct Answer  $3500

Solution & Explanation

Solution

Given,

Amount (A) = $4060

Rate of Simple Interest (R) = 4%

Time (T) = 4 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

$4060 = P (1 + 4% × 4)

⇒ $4060 = P (1 + ⁴/₁₀₀ × 4)

⇒ $4060 = P (1 + ^{4 × 4}/₁₀₀)

⇒ $4060 = P (1 + ¹⁶/₁₀₀)

⇒ $4060 = P (^{100 + 16}/₁₀₀)

⇒ $4060 = P × ¹¹⁶/₁₀₀

⇒ P × ¹¹⁶/₁₀₀ = $4060

⇒ P = ⁴⁰⁶⁰/_¹¹⁶/100

⇒ P = 4060 × ¹⁰⁰/₁₁₆

⇒ P = ^{4060 × 100}/₁₁₆

⇒ P = ⁴⁰⁶⁰⁰⁰/₁₁₆

⇒ 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 = 4 years

So, we need to calculate the simple interest for the given time period, which is 4 years

Thus, Simple Interest for 4 years = 4 × Simple Interest for 1 year

= 4 × 4 = 16

Thus, simple interest for 4 years = 16

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 16 = 116

Calculation of the Principal

Now,

∵ If the Amount is 116, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₁₆

∴ If the Amount is 4060, then the Principal = ¹⁰⁰/₁₁₆ × 4060

= ^{100 × 4060}/₁₁₆

= ⁴⁰⁶⁰⁰⁰/₁₁₆

= 3500

Thus, Principal = $3500

Thus, the sum borrowed = $3500 Answer

Similar Questions

(1) Michael took a loan of $4600 at the rate of 6% simple interest per annum. If he paid an amount of $6808 to clear the loan, then find the time period of the loan.

(2) 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.

(3) How much loan did Sharon borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8525 to clear it?

(4) Susan took a loan of $5300 at the rate of 10% simple interest per annum. If he paid an amount of $9010 to clear the loan, then find the time period of the loan.

(5) Find the amount to be paid if Michael borrowed a sum of $5300 at 6% simple interest for 7 years.

(6) In how much time a principal of $3000 will amount to $3300 at a simple interest of 5% per annum?

(7) Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 5% simple interest.

(8) Jessica took a loan of $5500 at the rate of 10% simple interest per annum. If he paid an amount of $9900 to clear the loan, then find the time period of the loan.

(9) James took a loan of $4000 at the rate of 10% simple interest per annum. If he paid an amount of $6400 to clear the loan, then find the time period of the loan.

(10) What amount does Jennifer have to pay after 6 years if he takes a loan of $3250 at 3% simple interest?