Simple Interest
Math MCQs

Question :    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.

Correct Answer  $3000

Solution & Explanation

Solution

Given,

Amount (A) = $3450

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

$3450 = P (1 + 5% × 3)

⇒ $3450 = P (1 + ⁵/₁₀₀ × 3)

⇒ $3450 = P (1 + ^{5 × 3}/₁₀₀)

⇒ $3450 = P (1 + ¹⁵/₁₀₀)

⇒ $3450 = P (^{100 + 15}/₁₀₀)

⇒ $3450 = P × ¹¹⁵/₁₀₀

⇒ P × ¹¹⁵/₁₀₀ = $3450

⇒ P = ³⁴⁵⁰/_¹¹⁵/100

⇒ P = 3450 × ¹⁰⁰/₁₁₅

⇒ P = ^{3450 × 100}/₁₁₅

⇒ P = ³⁴⁵⁰⁰⁰/₁₁₅

⇒ P = $3000

Thus, the sum borrowed (P) = $3000 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 3450, then the Principal = ¹⁰⁰/₁₁₅ × 3450

= ^{100 × 3450}/₁₁₅

= ³⁴⁵⁰⁰⁰/₁₁₅

= 3000

Thus, Principal = $3000

Thus, the sum borrowed = $3000 Answer

Similar Questions

(1) Calculate the amount due if Michael borrowed a sum of $3300 at 6% simple interest for 3 years.

(2) Robert took a loan of $4200 at the rate of 8% simple interest per annum. If he paid an amount of $6216 to clear the loan, then find the time period of the loan.

(3) James had to pay $3360 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(4) Betty took a loan of $6500 at the rate of 7% simple interest per annum. If he paid an amount of $9685 to clear the loan, then find the time period of the loan.

(5) Find the amount to be paid if Sarah borrowed a sum of $5850 at 8% simple interest for 8 years.

(6) How much loan did Timothy borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8880 to clear it?

(7) Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 8% simple interest.

(8) If Linda borrowed $3350 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.

(9) Calculate the amount due if John borrowed a sum of $3200 at 10% simple interest for 4 years.

(10) Nancy took a loan of $6300 at the rate of 8% simple interest per annum. If he paid an amount of $9324 to clear the loan, then find the time period of the loan.