Simple Interest
Math MCQs

Question :    If Ashley paid $4914 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

Correct Answer  $4550

Solution & Explanation

Solution

Given,

Amount (A) = $4914

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

$4914 = P (1 + 2% × 4)

⇒ $4914 = P (1 + ²/₁₀₀ × 4)

⇒ $4914 = P (1 + ^{2 × 4}/₁₀₀)

⇒ $4914 = P (1 + ⁸/₁₀₀)

⇒ $4914 = P (^{100 + 8}/₁₀₀)

⇒ $4914 = P × ¹⁰⁸/₁₀₀

⇒ P × ¹⁰⁸/₁₀₀ = $4914

⇒ P = ⁴⁹¹⁴/_¹⁰⁸/100

⇒ P = 4914 × ¹⁰⁰/₁₀₈

⇒ P = ^{4914 × 100}/₁₀₈

⇒ P = ⁴⁹¹⁴⁰⁰/₁₀₈

⇒ P = $4550

Thus, the sum borrowed (P) = $4550 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 4914, then the Principal = ¹⁰⁰/₁₀₈ × 4914

= ^{100 × 4914}/₁₀₈

= ⁴⁹¹⁴⁰⁰/₁₀₈

= 4550

Thus, Principal = $4550

Thus, the sum borrowed = $4550 Answer

Similar Questions

(1) Calculate the amount due if Christopher borrowed a sum of $4000 at 5% simple interest for 3 years.

(2) What amount does Patricia have to pay after 5 years if he takes a loan of $3150 at 8% simple interest?

(3) Calculate the amount due if David borrowed a sum of $3400 at 4% simple interest for 3 years.

(4) If Patricia paid $3780 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(5) If Christopher paid $4480 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(6) Jennifer took a loan of $4500 at the rate of 6% simple interest per annum. If he paid an amount of $7200 to clear the loan, then find the time period of the loan.

(7) Calculate the amount due if Joseph borrowed a sum of $3700 at 2% simple interest for 4 years.

(8) Calculate the amount due after 9 years if Sarah borrowed a sum of $5850 at a rate of 3% simple interest.

(9) Calculate the amount due after 10 years if Susan borrowed a sum of $5650 at a rate of 8% simple interest.

(10) William took a loan of $5000 at the rate of 10% simple interest per annum. If he paid an amount of $8500 to clear the loan, then find the time period of the loan.