Simple Interest
Math MCQs

Question :    Kimberly had to pay $5347.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

Correct Answer  $4650

Solution & Explanation

Solution

Given,

Amount (A) = $5347.5

Rate of Simple Interest (R) = 5%

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

$5347.5 = P (1 + 5% × 3)

⇒ $5347.5 = P (1 + ⁵/₁₀₀ × 3)

⇒ $5347.5 = P (1 + ^{5 × 3}/₁₀₀)

⇒ $5347.5 = P (1 + ¹⁵/₁₀₀)

⇒ $5347.5 = P (^{100 + 15}/₁₀₀)

⇒ $5347.5 = P × ¹¹⁵/₁₀₀

⇒ P × ¹¹⁵/₁₀₀ = $5347.5

⇒ P = ^5347.5/_¹¹⁵/100

⇒ P = 5347.5 × ¹⁰⁰/₁₁₅

⇒ P = ^{5347.5 × 100}/₁₁₅

⇒ P = ⁵³⁴⁷⁵⁰/₁₁₅

⇒ P = $4650

Thus, the sum borrowed (P) = $4650 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 = 5% per annum

Thus, Interest = 5% of principal

⇒ Interest = 5% of 100 = 5

Thus, Simple Interest for 1 year = 5

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 × 5 = 15

Thus, simple interest for 3 years = 15

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 15 = 115

Calculation of the Principal

Now,

∵ If the Amount is 115, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₁₅

∴ If the Amount is 5347.5, then the Principal = ¹⁰⁰/₁₁₅ × 5347.5

= ^{100 × 5347.5}/₁₁₅

= ⁵³⁴⁷⁵⁰/₁₁₅

= 4650

Thus, Principal = $4650

Thus, the sum borrowed = $4650 Answer

Similar Questions

(1) Find the amount to be paid if Sarah borrowed a sum of $5850 at 3% simple interest for 7 years.

(2) Calculate the amount due if Sarah borrowed a sum of $3850 at 4% simple interest for 4 years.

(3) Calculate the amount due if Joseph borrowed a sum of $3700 at 7% simple interest for 3 years.

(4) John took a loan of $4400 at the rate of 9% simple interest per annum. If he paid an amount of $7172 to clear the loan, then find the time period of the loan.

(5) Susan took a loan of $5300 at the rate of 7% simple interest per annum. If he paid an amount of $7526 to clear the loan, then find the time period of the loan.

(6) Calculate the amount due if Linda borrowed a sum of $3350 at 9% simple interest for 3 years.

(7) James had to pay $3450 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(8) John took a loan of $4400 at the rate of 8% simple interest per annum. If he paid an amount of $7568 to clear the loan, then find the time period of the loan.

(9) Mary took a loan of $4100 at the rate of 7% simple interest per annum. If he paid an amount of $6683 to clear the loan, then find the time period of the loan.

(10) Calculate the amount due if Patricia borrowed a sum of $3150 at 5% simple interest for 4 years.