Simple Interest
Math MCQs

Question :    If Christopher paid $4800 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

Correct Answer  $4000

Solution & Explanation

Solution

Given,

Amount (A) = $4800

Rate of Simple Interest (R) = 5%

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

$4800 = P (1 + 5% × 4)

⇒ $4800 = P (1 + ⁵/₁₀₀ × 4)

⇒ $4800 = P (1 + ^{5 × 4}/₁₀₀)

⇒ $4800 = P (1 + ²⁰/₁₀₀)

⇒ $4800 = P (^{100 + 20}/₁₀₀)

⇒ $4800 = P × ¹²⁰/₁₀₀

⇒ P × ¹²⁰/₁₀₀ = $4800

⇒ P = ⁴⁸⁰⁰/_¹²⁰/100

⇒ P = 4800 × ¹⁰⁰/₁₂₀

⇒ P = ^{4800 × 100}/₁₂₀

⇒ P = ⁴⁸⁰⁰⁰⁰/₁₂₀

⇒ P = $4000

Thus, the sum borrowed (P) = $4000 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 = 5% per annum

Thus, Interest = 5% of principal

⇒ Interest = 5% of 100 = 5

Thus, Simple Interest for 1 year = 5

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 × 5 = 20

Thus, simple interest for 4 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 4800, then the Principal = ¹⁰⁰/₁₂₀ × 4800

= ^{100 × 4800}/₁₂₀

= ⁴⁸⁰⁰⁰⁰/₁₂₀

= 4000

Thus, Principal = $4000

Thus, the sum borrowed = $4000 Answer

Similar Questions

(1) Kimberly had to pay $5208 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(2) If Anthony paid $4644 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(3) Calculate the amount due if Christopher borrowed a sum of $4000 at 3% simple interest for 4 years.

(4) How much loan did Steven borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7260 to clear it?

(5) Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 10% simple interest.

(6) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 10% simple interest?

(7) James took a loan of $4000 at the rate of 9% simple interest per annum. If he paid an amount of $6160 to clear the loan, then find the time period of the loan.

(8) James took a loan of $4000 at the rate of 9% simple interest per annum. If he paid an amount of $6520 to clear the loan, then find the time period of the loan.

(9) What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 7% simple interest?

(10) Calculate the amount due after 10 years if Thomas borrowed a sum of $5800 at a rate of 8% simple interest.