Simple Interest
Math MCQs

Question :    If Donald paid $4860 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

Correct Answer  $4500

Solution & Explanation

Solution

Given,

Amount (A) = $4860

Rate of Simple Interest (R) = 2%

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

$4860 = P (1 + 2% × 4)

⇒ $4860 = P (1 + ²/₁₀₀ × 4)

⇒ $4860 = P (1 + ^{2 × 4}/₁₀₀)

⇒ $4860 = P (1 + ⁸/₁₀₀)

⇒ $4860 = P (^{100 + 8}/₁₀₀)

⇒ $4860 = P × ¹⁰⁸/₁₀₀

⇒ P × ¹⁰⁸/₁₀₀ = $4860

⇒ P = ⁴⁸⁶⁰/_¹⁰⁸/100

⇒ P = 4860 × ¹⁰⁰/₁₀₈

⇒ P = ^{4860 × 100}/₁₀₈

⇒ P = ⁴⁸⁶⁰⁰⁰/₁₀₈

⇒ P = $4500

Thus, the sum borrowed (P) = $4500 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 = 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 × 2 = 8

Thus, simple interest for 4 years = 8

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 8 = 108

Calculation of the Principal

Now,

∵ If the Amount is 108, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₀₈

∴ If the Amount is 4860, then the Principal = ¹⁰⁰/₁₀₈ × 4860

= ^{100 × 4860}/₁₀₈

= ⁴⁸⁶⁰⁰⁰/₁₀₈

= 4500

Thus, Principal = $4500

Thus, the sum borrowed = $4500 Answer

Similar Questions

(1) Calculate the amount due if William borrowed a sum of $3500 at 2% simple interest for 3 years.

(2) Margaret took a loan of $6700 at the rate of 8% simple interest per annum. If he paid an amount of $12060 to clear the loan, then find the time period of the loan.

(3) Find the amount to be paid if Susan borrowed a sum of $5650 at 7% simple interest for 7 years.

(4) Find the amount to be paid if Patricia borrowed a sum of $5150 at 4% simple interest for 7 years.

(5) Calculate the amount due after 9 years if Michael borrowed a sum of $5300 at a rate of 6% simple interest.

(6) Calculate the amount due if Barbara borrowed a sum of $3550 at 7% simple interest for 3 years.

(7) If Betty paid $4930 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(8) Find the amount to be paid if Joseph borrowed a sum of $5700 at 2% simple interest for 7 years.

(9) Calculate the amount due after 9 years if Michael borrowed a sum of $5300 at a rate of 3% simple interest.

(10) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 4% simple interest?