Simple Interest
Math MCQs

Question :    If Lisa paid $4698 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

Correct Answer  $4050

Solution & Explanation

Solution

Given,

Amount (A) = $4698

Rate of Simple Interest (R) = 4%

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

$4698 = P (1 + 4% × 4)

⇒ $4698 = P (1 + ⁴/₁₀₀ × 4)

⇒ $4698 = P (1 + ^{4 × 4}/₁₀₀)

⇒ $4698 = P (1 + ¹⁶/₁₀₀)

⇒ $4698 = P (^{100 + 16}/₁₀₀)

⇒ $4698 = P × ¹¹⁶/₁₀₀

⇒ P × ¹¹⁶/₁₀₀ = $4698

⇒ P = ⁴⁶⁹⁸/_¹¹⁶/100

⇒ P = 4698 × ¹⁰⁰/₁₁₆

⇒ P = ^{4698 × 100}/₁₁₆

⇒ P = ⁴⁶⁹⁸⁰⁰/₁₁₆

⇒ P = $4050

Thus, the sum borrowed (P) = $4050 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 = 4% per annum

Thus, Interest = 4% of principal

⇒ Interest = 4% of 100 = 4

Thus, Simple Interest for 1 year = 4

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 × 4 = 16

Thus, simple interest for 4 years = 16

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 16 = 116

Calculation of the Principal

Now,

∵ If the Amount is 116, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₁₆

∴ If the Amount is 4698, then the Principal = ¹⁰⁰/₁₁₆ × 4698

= ^{100 × 4698}/₁₁₆

= ⁴⁶⁹⁸⁰⁰/₁₁₆

= 4050

Thus, Principal = $4050

Thus, the sum borrowed = $4050 Answer

Similar Questions

(1) Robert took a loan of $4200 at the rate of 8% simple interest per annum. If he paid an amount of $6552 to clear the loan, then find the time period of the loan.

(2) How much loan did Nancy borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7687.5 to clear it?

(3) If Robert paid $3720 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(4) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 9% simple interest for 8 years.

(5) Christopher took a loan of $6000 at the rate of 9% simple interest per annum. If he paid an amount of $9240 to clear the loan, then find the time period of the loan.

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

(7) What amount does William have to pay after 6 years if he takes a loan of $3500 at 3% simple interest?

(8) How much loan did James borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6250 to clear it?

(9) Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 6% simple interest.

(10) What amount will be due after 2 years if Mark borrowed a sum of $3700 at a 8% simple interest?