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) Susan took a loan of $5300 at the rate of 7% simple interest per annum. If he paid an amount of $8268 to clear the loan, then find the time period of the loan.

(2) Calculate the amount due if Richard borrowed a sum of $3600 at 6% simple interest for 3 years.

(3) If Michael paid $3564 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(4) Anthony took a loan of $6600 at the rate of 10% simple interest per annum. If he paid an amount of $13200 to clear the loan, then find the time period of the loan.

(5) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 7% simple interest?

(6) Calculate the amount due after 9 years if Barbara borrowed a sum of $5550 at a rate of 2% simple interest.

(7) How much loan did John borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6240 to clear it?

(8) What amount does James have to pay after 6 years if he takes a loan of $3000 at 3% simple interest?

(9) Richard took a loan of $5200 at the rate of 7% simple interest per annum. If he paid an amount of $7748 to clear the loan, then find the time period of the loan.

(10) Find the amount to be paid if Karen borrowed a sum of $5950 at 4% simple interest for 8 years.