Simple Interest
Math MCQs

Question :    If Christopher paid $4640 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

Correct Answer  $4000

Solution & Explanation

Solution

Given,

Amount (A) = $4640

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

$4640 = P (1 + 4% × 4)

⇒ $4640 = P (1 + ⁴/₁₀₀ × 4)

⇒ $4640 = P (1 + ^{4 × 4}/₁₀₀)

⇒ $4640 = P (1 + ¹⁶/₁₀₀)

⇒ $4640 = P (^{100 + 16}/₁₀₀)

⇒ $4640 = P × ¹¹⁶/₁₀₀

⇒ P × ¹¹⁶/₁₀₀ = $4640

⇒ P = ⁴⁶⁴⁰/_¹¹⁶/100

⇒ P = 4640 × ¹⁰⁰/₁₁₆

⇒ P = ^{4640 × 100}/₁₁₆

⇒ P = ⁴⁶⁴⁰⁰⁰/₁₁₆

⇒ P = $4000

Thus, the sum borrowed (P) = $4000 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 4640, then the Principal = ¹⁰⁰/₁₁₆ × 4640

= ^{100 × 4640}/₁₁₆

= ⁴⁶⁴⁰⁰⁰/₁₁₆

= 4000

Thus, Principal = $4000

Thus, the sum borrowed = $4000 Answer

Similar Questions

(1) Calculate the amount due if Linda borrowed a sum of $3350 at 3% simple interest for 3 years.

(2) Patricia took a loan of $4300 at the rate of 10% simple interest per annum. If he paid an amount of $8600 to clear the loan, then find the time period of the loan.

(3) Daniel took a loan of $6200 at the rate of 8% simple interest per annum. If he paid an amount of $10664 to clear the loan, then find the time period of the loan.

(4) What amount will be due after 2 years if David borrowed a sum of $3200 at a 5% simple interest?

(5) What amount does Jennifer have to pay after 5 years if he takes a loan of $3250 at 2% simple interest?

(6) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 7% simple interest for 8 years.

(7) How much loan did James borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6000 to clear it?

(8) Find the amount to be paid if David borrowed a sum of $5400 at 6% simple interest for 8 years.

(9) Thomas took a loan of $5600 at the rate of 8% simple interest per annum. If he paid an amount of $10080 to clear the loan, then find the time period of the loan.

(10) Matthew had to pay $4452 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.