Simple Interest
Math MCQs

Question :    Mary had to pay $3507.5 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  $3050

Solution & Explanation

Solution

Given,

Amount (A) = $3507.5

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

$3507.5 = P (1 + 5% × 3)

⇒ $3507.5 = P (1 + ⁵/₁₀₀ × 3)

⇒ $3507.5 = P (1 + ^{5 × 3}/₁₀₀)

⇒ $3507.5 = P (1 + ¹⁵/₁₀₀)

⇒ $3507.5 = P (^{100 + 15}/₁₀₀)

⇒ $3507.5 = P × ¹¹⁵/₁₀₀

⇒ P × ¹¹⁵/₁₀₀ = $3507.5

⇒ P = ^3507.5/_¹¹⁵/100

⇒ P = 3507.5 × ¹⁰⁰/₁₁₅

⇒ P = ^{3507.5 × 100}/₁₁₅

⇒ P = ³⁵⁰⁷⁵⁰/₁₁₅

⇒ P = $3050

Thus, the sum borrowed (P) = $3050 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 3507.5, then the Principal = ¹⁰⁰/₁₁₅ × 3507.5

= ^{100 × 3507.5}/₁₁₅

= ³⁵⁰⁷⁵⁰/₁₁₅

= 3050

Thus, Principal = $3050

Thus, the sum borrowed = $3050 Answer

Similar Questions

(1) Sandra took a loan of $6900 at the rate of 10% simple interest per annum. If he paid an amount of $11040 to clear the loan, then find the time period of the loan.

(2) Joseph took a loan of $5400 at the rate of 8% simple interest per annum. If he paid an amount of $7992 to clear the loan, then find the time period of the loan.

(3) Sarah took a loan of $5700 at the rate of 9% simple interest per annum. If he paid an amount of $8778 to clear the loan, then find the time period of the loan.

(4) If Michael borrowed $3300 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.

(5) Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 6% simple interest.

(6) Calculate the amount due after 9 years if Barbara borrowed a sum of $5550 at a rate of 3% simple interest.

(7) Calculate the amount due after 10 years if Susan borrowed a sum of $5650 at a rate of 9% simple interest.

(8) Thomas had to pay $4028 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(9) Calculate the amount due if Jessica borrowed a sum of $3750 at 8% simple interest for 4 years.

(10) Calculate the amount due after 10 years if Sarah borrowed a sum of $5850 at a rate of 6% simple interest.