Simple Interest
Math MCQs

Question :    If Donald paid $5220 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

Correct Answer  $4500

Solution & Explanation

Solution

Given,

Amount (A) = $5220

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

$5220 = P (1 + 4% × 4)

⇒ $5220 = P (1 + ⁴/₁₀₀ × 4)

⇒ $5220 = P (1 + ^{4 × 4}/₁₀₀)

⇒ $5220 = P (1 + ¹⁶/₁₀₀)

⇒ $5220 = P (^{100 + 16}/₁₀₀)

⇒ $5220 = P × ¹¹⁶/₁₀₀

⇒ P × ¹¹⁶/₁₀₀ = $5220

⇒ P = ⁵²²⁰/_¹¹⁶/100

⇒ P = 5220 × ¹⁰⁰/₁₁₆

⇒ P = ^{5220 × 100}/₁₁₆

⇒ P = ⁵²²⁰⁰⁰/₁₁₆

⇒ P = $4500

Thus, the sum borrowed (P) = $4500 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 5220, then the Principal = ¹⁰⁰/₁₁₆ × 5220

= ^{100 × 5220}/₁₁₆

= ⁵²²⁰⁰⁰/₁₁₆

= 4500

Thus, Principal = $4500

Thus, the sum borrowed = $4500 Answer

Similar Questions

(1) In how much time a principal of $3050 will amount to $3294 at a simple interest of 4% per annum?

(2) David took a loan of $4800 at the rate of 10% simple interest per annum. If he paid an amount of $8640 to clear the loan, then find the time period of the loan.

(3) If Linda paid $3886 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(4) Charles had to pay $4485 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(5) Find the amount to be paid if Richard borrowed a sum of $5600 at 4% simple interest for 7 years.

(6) Mark took a loan of $6800 at the rate of 9% simple interest per annum. If he paid an amount of $10472 to clear the loan, then find the time period of the loan.

(7) Thomas took a loan of $5600 at the rate of 8% simple interest per annum. If he paid an amount of $8736 to clear the loan, then find the time period of the loan.

(8) Calculate the amount due if David borrowed a sum of $3400 at 5% simple interest for 4 years.

(9) How much loan did Cynthia borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $9142.5 to clear it?

(10) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 4% simple interest?