Simple Interest
Math MCQs

Question :    If Anthony paid $4988 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

Correct Answer  $4300

Solution & Explanation

Solution

Given,

Amount (A) = $4988

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

$4988 = P (1 + 4% × 4)

⇒ $4988 = P (1 + ⁴/₁₀₀ × 4)

⇒ $4988 = P (1 + ^{4 × 4}/₁₀₀)

⇒ $4988 = P (1 + ¹⁶/₁₀₀)

⇒ $4988 = P (^{100 + 16}/₁₀₀)

⇒ $4988 = P × ¹¹⁶/₁₀₀

⇒ P × ¹¹⁶/₁₀₀ = $4988

⇒ P = ⁴⁹⁸⁸/_¹¹⁶/100

⇒ P = 4988 × ¹⁰⁰/₁₁₆

⇒ P = ^{4988 × 100}/₁₁₆

⇒ P = ⁴⁹⁸⁸⁰⁰/₁₁₆

⇒ P = $4300

Thus, the sum borrowed (P) = $4300 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 4988, then the Principal = ¹⁰⁰/₁₁₆ × 4988

= ^{100 × 4988}/₁₁₆

= ⁴⁹⁸⁸⁰⁰/₁₁₆

= 4300

Thus, Principal = $4300

Thus, the sum borrowed = $4300 Answer

Similar Questions

(1) How much loan did Elizabeth borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6267.5 to clear it?

(2) Lisa took a loan of $6100 at the rate of 8% simple interest per annum. If he paid an amount of $10004 to clear the loan, then find the time period of the loan.

(3) How much loan did Linda borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6152.5 to clear it?

(4) What amount will be due after 2 years if John borrowed a sum of $3100 at a 8% simple interest?

(5) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 10% simple interest for 7 years.

(6) Find the amount to be paid if Karen borrowed a sum of $5950 at 10% simple interest for 7 years.

(7) Calculate the amount due after 9 years if Elizabeth borrowed a sum of $5450 at a rate of 9% simple interest.

(8) What amount will be due after 2 years if Donald borrowed a sum of $3750 at a 6% simple interest?

(9) Find the amount to be paid if Susan borrowed a sum of $5650 at 10% simple interest for 7 years.

(10) Patricia took a loan of $4300 at the rate of 9% simple interest per annum. If he paid an amount of $7396 to clear the loan, then find the time period of the loan.