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) Margaret took a loan of $6700 at the rate of 10% simple interest per annum. If he paid an amount of $13400 to clear the loan, then find the time period of the loan.

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

(3) How much loan did Andrew borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7820 to clear it?

(4) Christopher took a loan of $6000 at the rate of 6% simple interest per annum. If he paid an amount of $9600 to clear the loan, then find the time period of the loan.

(5) Find the amount to be paid if Karen borrowed a sum of $5950 at 2% simple interest for 7 years.

(6) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 9% simple interest for 7 years.

(7) Calculate the amount due after 9 years if Jessica borrowed a sum of $5750 at a rate of 2% simple interest.

(8) What amount does Thomas have to pay after 5 years if he takes a loan of $3800 at 2% simple interest?

(9) Calculate the amount due after 9 years if Michael borrowed a sum of $5300 at a rate of 7% simple interest.

(10) How much loan did Ashley borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7532.5 to clear it?