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) Christopher took a loan of $6000 at the rate of 9% simple interest per annum. If he paid an amount of $9240 to clear the loan, then find the time period of the loan.

(2) If Steven paid $5152 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(3) Calculate the amount due if John borrowed a sum of $3200 at 6% simple interest for 4 years.

(4) Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 7% simple interest.

(5) How much loan did James borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $5750 to clear it?

(6) Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 3% simple interest.

(7) Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 8% simple interest.

(8) Calculate the amount due if Susan borrowed a sum of $3650 at 9% simple interest for 4 years.

(9) Calculate the amount due after 10 years if Jessica borrowed a sum of $5750 at a rate of 3% simple interest.

(10) Nancy took a loan of $6300 at the rate of 10% simple interest per annum. If he paid an amount of $10710 to clear the loan, then find the time period of the loan.