Simple Interest
Math MCQs

Question :    Emily had to pay $5320 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  $4750

Solution & Explanation

Solution

Given,

Amount (A) = $5320

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

$5320 = P (1 + 4% × 3)

⇒ $5320 = P (1 + ⁴/₁₀₀ × 3)

⇒ $5320 = P (1 + ^{4 × 3}/₁₀₀)

⇒ $5320 = P (1 + ¹²/₁₀₀)

⇒ $5320 = P (^{100 + 12}/₁₀₀)

⇒ $5320 = P × ¹¹²/₁₀₀

⇒ P × ¹¹²/₁₀₀ = $5320

⇒ P = ⁵³²⁰/_¹¹²/100

⇒ P = 5320 × ¹⁰⁰/₁₁₂

⇒ P = ^{5320 × 100}/₁₁₂

⇒ P = ⁵³²⁰⁰⁰/₁₁₂

⇒ P = $4750

Thus, the sum borrowed (P) = $4750 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 5320, then the Principal = ¹⁰⁰/₁₁₂ × 5320

= ^{100 × 5320}/₁₁₂

= ⁵³²⁰⁰⁰/₁₁₂

= 4750

Thus, Principal = $4750

Thus, the sum borrowed = $4750 Answer

Similar Questions

(1) Charles took a loan of $5800 at the rate of 7% simple interest per annum. If he paid an amount of $9860 to clear the loan, then find the time period of the loan.

(2) Mark took a loan of $6800 at the rate of 10% simple interest per annum. If he paid an amount of $11560 to clear the loan, then find the time period of the loan.

(3) Mary took a loan of $4100 at the rate of 10% simple interest per annum. If he paid an amount of $6560 to clear the loan, then find the time period of the loan.

(4) 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.

(5) What amount will be due after 2 years if Steven borrowed a sum of $3800 at a 10% simple interest?

(6) If Matthew paid $4704 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(7) Calculate the amount due if Mary borrowed a sum of $3050 at 10% simple interest for 4 years.

(8) If Lisa paid $4374 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(9) Steven had to pay $5014 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(10) How much loan did Lisa borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7562.5 to clear it?