Simple Interest
Math MCQs

Question :    If Steven paid $4968 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

Correct Answer  $4600

Solution & Explanation

Solution

Given,

Amount (A) = $4968

Rate of Simple Interest (R) = 2%

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

$4968 = P (1 + 2% × 4)

⇒ $4968 = P (1 + ²/₁₀₀ × 4)

⇒ $4968 = P (1 + ^{2 × 4}/₁₀₀)

⇒ $4968 = P (1 + ⁸/₁₀₀)

⇒ $4968 = P (^{100 + 8}/₁₀₀)

⇒ $4968 = P × ¹⁰⁸/₁₀₀

⇒ P × ¹⁰⁸/₁₀₀ = $4968

⇒ P = ⁴⁹⁶⁸/_¹⁰⁸/100

⇒ P = 4968 × ¹⁰⁰/₁₀₈

⇒ P = ^{4968 × 100}/₁₀₈

⇒ P = ⁴⁹⁶⁸⁰⁰/₁₀₈

⇒ P = $4600

Thus, the sum borrowed (P) = $4600 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 = 2% per annum

Thus, Interest = 2% of principal

⇒ Interest = 2% of 100 = 2

Thus, Simple Interest for 1 year = 2

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 × 2 = 8

Thus, simple interest for 4 years = 8

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 8 = 108

Calculation of the Principal

Now,

∵ If the Amount is 108, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₀₈

∴ If the Amount is 4968, then the Principal = ¹⁰⁰/₁₀₈ × 4968

= ^{100 × 4968}/₁₀₈

= ⁴⁹⁶⁸⁰⁰/₁₀₈

= 4600

Thus, Principal = $4600

Thus, the sum borrowed = $4600 Answer

Similar Questions

(1) John took a loan of $4400 at the rate of 7% simple interest per annum. If he paid an amount of $6248 to clear the loan, then find the time period of the loan.

(2) How much loan did Michelle borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8687.5 to clear it?

(3) Calculate the amount due if Christopher borrowed a sum of $4000 at 2% simple interest for 3 years.

(4) What amount will be due after 2 years if John borrowed a sum of $3100 at a 9% simple interest?

(5) David took a loan of $4800 at the rate of 7% simple interest per annum. If he paid an amount of $7152 to clear the loan, then find the time period of the loan.

(6) Calculate the amount due if Robert borrowed a sum of $3100 at 4% simple interest for 4 years.

(7) What amount does Jennifer have to pay after 5 years if he takes a loan of $3250 at 8% simple interest?

(8) Anthony took a loan of $6600 at the rate of 10% simple interest per annum. If he paid an amount of $11220 to clear the loan, then find the time period of the loan.

(9) Karen took a loan of $5900 at the rate of 8% simple interest per annum. If he paid an amount of $8732 to clear the loan, then find the time period of the loan.

(10) In how much time a principal of $3050 will amount to $3660 at a simple interest of 5% per annum?