Simple Interest
Math MCQs

Question :    Mark had to pay $4928 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

Correct Answer  $4400

Solution & Explanation

Solution

Given,

Amount (A) = $4928

Rate of Simple Interest (R) = 4%

Time (T) = 3 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

$4928 = P (1 + 4% × 3)

⇒ $4928 = P (1 + ⁴/₁₀₀ × 3)

⇒ $4928 = P (1 + ^{4 × 3}/₁₀₀)

⇒ $4928 = P (1 + ¹²/₁₀₀)

⇒ $4928 = P (^{100 + 12}/₁₀₀)

⇒ $4928 = P × ¹¹²/₁₀₀

⇒ P × ¹¹²/₁₀₀ = $4928

⇒ P = ⁴⁹²⁸/_¹¹²/100

⇒ P = 4928 × ¹⁰⁰/₁₁₂

⇒ P = ^{4928 × 100}/₁₁₂

⇒ P = ⁴⁹²⁸⁰⁰/₁₁₂

⇒ P = $4400

Thus, the sum borrowed (P) = $4400 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 = 3 years

So, we need to calculate the simple interest for the given time period, which is 3 years

Thus, Simple Interest for 3 years = 3 × Simple Interest for 1 year

= 3 × 4 = 12

Thus, simple interest for 3 years = 12

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 12 = 112

Calculation of the Principal

Now,

∵ If the Amount is 112, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₁₂

∴ If the Amount is 4928, then the Principal = ¹⁰⁰/₁₁₂ × 4928

= ^{100 × 4928}/₁₁₂

= ⁴⁹²⁸⁰⁰/₁₁₂

= 4400

Thus, Principal = $4400

Thus, the sum borrowed = $4400 Answer

Similar Questions

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

(2) If James paid $3360 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(3) Daniel took a loan of $6200 at the rate of 6% simple interest per annum. If he paid an amount of $9548 to clear the loan, then find the time period of the loan.

(4) How much loan did Nancy borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7380 to clear it?

(5) If Charles paid $4680 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(6) Jennifer took a loan of $4500 at the rate of 6% simple interest per annum. If he paid an amount of $6660 to clear the loan, then find the time period of the loan.

(7) Nancy took a loan of $6300 at the rate of 6% simple interest per annum. If he paid an amount of $8568 to clear the loan, then find the time period of the loan.

(8) Find the amount to be paid if Patricia borrowed a sum of $5150 at 2% simple interest for 8 years.

(9) Mary took a loan of $4100 at the rate of 9% simple interest per annum. If he paid an amount of $7052 to clear the loan, then find the time period of the loan.

(10) 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?