Simple Interest
Math MCQs

Question :    If Lisa paid $4860 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

Correct Answer  $4050

Solution & Explanation

Solution

Given,

Amount (A) = $4860

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

$4860 = P (1 + 5% × 4)

⇒ $4860 = P (1 + ⁵/₁₀₀ × 4)

⇒ $4860 = P (1 + ^{5 × 4}/₁₀₀)

⇒ $4860 = P (1 + ²⁰/₁₀₀)

⇒ $4860 = P (^{100 + 20}/₁₀₀)

⇒ $4860 = P × ¹²⁰/₁₀₀

⇒ P × ¹²⁰/₁₀₀ = $4860

⇒ P = ⁴⁸⁶⁰/_¹²⁰/100

⇒ P = 4860 × ¹⁰⁰/₁₂₀

⇒ P = ^{4860 × 100}/₁₂₀

⇒ P = ⁴⁸⁶⁰⁰⁰/₁₂₀

⇒ 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 = 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 4860, then the Principal = ¹⁰⁰/₁₂₀ × 4860

= ^{100 × 4860}/₁₂₀

= ⁴⁸⁶⁰⁰⁰/₁₂₀

= 4050

Thus, Principal = $4050

Thus, the sum borrowed = $4050 Answer

Similar Questions

(1) Donald took a loan of $7000 at the rate of 7% simple interest per annum. If he paid an amount of $10430 to clear the loan, then find the time period of the loan.

(2) Find the amount to be paid if James borrowed a sum of $5000 at 8% simple interest for 8 years.

(3) How much loan did Melissa borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8452.5 to clear it?

(4) Calculate the amount due if Michael borrowed a sum of $3300 at 9% simple interest for 4 years.

(5) Calculate the amount due if Barbara borrowed a sum of $3550 at 5% simple interest for 3 years.

(6) Calculate the amount due after 9 years if Jessica borrowed a sum of $5750 at a rate of 5% simple interest.

(7) Calculate the amount due if Sarah borrowed a sum of $3850 at 5% simple interest for 4 years.

(8) James took a loan of $4000 at the rate of 10% simple interest per annum. If he paid an amount of $8000 to clear the loan, then find the time period of the loan.

(9) What amount does Thomas have to pay after 6 years if he takes a loan of $3800 at 9% simple interest?

(10) Find the amount to be paid if Robert borrowed a sum of $5100 at 4% simple interest for 7 years.