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) What amount will be due after 2 years if Kenneth borrowed a sum of $4000 at a 10% simple interest?

(2) Susan had to pay $4088 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(3) Calculate the amount due if Susan borrowed a sum of $3650 at 5% simple interest for 4 years.

(4) Find the amount to be paid if Patricia borrowed a sum of $5150 at 6% simple interest for 8 years.

(5) William took a loan of $5000 at the rate of 6% simple interest per annum. If he paid an amount of $7400 to clear the loan, then find the time period of the loan.

(6) How much loan did Lisa borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6957.5 to clear it?

(7) Mary took a loan of $4100 at the rate of 9% simple interest per annum. If he paid an amount of $6683 to clear the loan, then find the time period of the loan.

(8) Find the amount to be paid if Michael borrowed a sum of $5300 at 5% simple interest for 7 years.

(9) Calculate the amount due if Charles borrowed a sum of $3900 at 5% simple interest for 4 years.

(10) Calculate the amount due if Karen borrowed a sum of $3950 at 9% simple interest for 3 years.