Simple Interest
Math MCQs

Question :    If Matthew paid $5040 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

Correct Answer  $4200

Solution & Explanation

Solution

Given,

Amount (A) = $5040

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

$5040 = P (1 + 5% × 4)

⇒ $5040 = P (1 + ⁵/₁₀₀ × 4)

⇒ $5040 = P (1 + ^{5 × 4}/₁₀₀)

⇒ $5040 = P (1 + ²⁰/₁₀₀)

⇒ $5040 = P (^{100 + 20}/₁₀₀)

⇒ $5040 = P × ¹²⁰/₁₀₀

⇒ P × ¹²⁰/₁₀₀ = $5040

⇒ P = ⁵⁰⁴⁰/_¹²⁰/100

⇒ P = 5040 × ¹⁰⁰/₁₂₀

⇒ P = ^{5040 × 100}/₁₂₀

⇒ P = ⁵⁰⁴⁰⁰⁰/₁₂₀

⇒ P = $4200

Thus, the sum borrowed (P) = $4200 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 5040, then the Principal = ¹⁰⁰/₁₂₀ × 5040

= ^{100 × 5040}/₁₂₀

= ⁵⁰⁴⁰⁰⁰/₁₂₀

= 4200

Thus, Principal = $4200

Thus, the sum borrowed = $4200 Answer

Similar Questions

(1) Lisa had to pay $4536 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(2) What amount will be due after 2 years if Kenneth borrowed a sum of $4000 at a 9% simple interest?

(3) Find the amount to be paid if Linda borrowed a sum of $5350 at 6% simple interest for 7 years.

(4) Calculate the amount due after 10 years if Robert borrowed a sum of $5100 at a rate of 3% simple interest.

(5) Calculate the amount due after 9 years if Joseph borrowed a sum of $5700 at a rate of 3% simple interest.

(6) Charles took a loan of $5800 at the rate of 7% simple interest per annum. If he paid an amount of $8236 to clear the loan, then find the time period of the loan.

(7) Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 3% simple interest.

(8) Elizabeth took a loan of $4900 at the rate of 10% simple interest per annum. If he paid an amount of $9800 to clear the loan, then find the time period of the loan.

(9) If Mark paid $4752 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(10) How much loan did David borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6210 to clear it?