Simple Interest
Math MCQs

Question :    How much loan did Dorothy borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8337.5 to clear it?

Correct Answer  $7250

Solution & Explanation

Solution

Given,

Amount (A) = $8337.5

Rate of Simple Interest (R) = 3%

Time (T) = 5 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

$8337.5 = P (1 + 3% × 5)

⇒ $8337.5 = P (1 + ³/₁₀₀ × 5)

⇒ $8337.5 = P (1 + ^{3 × 5}/₁₀₀)

⇒ $8337.5 = P (1 + ¹⁵/₁₀₀)

⇒ $8337.5 = P (^{100 + 15}/₁₀₀)

⇒ $8337.5 = P × ¹¹⁵/₁₀₀

⇒ P × ¹¹⁵/₁₀₀ = $8337.5

⇒ P = ^8337.5/_¹¹⁵/100

⇒ P = 8337.5 × ¹⁰⁰/₁₁₅

⇒ P = ^{8337.5 × 100}/₁₁₅

⇒ P = ⁸³³⁷⁵⁰/₁₁₅

⇒ P = $7250

Thus, the sum borrowed (P) = $7250 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 = 3% per annum

Thus, Interest = 3% of principal

⇒ Interest = 3% of 100 = 3

Thus, Simple Interest for 1 year = 3

Calculation of the Amount

Since, in the question, time = 5 years

So, we need to calculate the simple interest for the given time period, which is 5 years

Thus, Simple Interest for 5 years = 5 × Simple Interest for 1 year

= 5 × 3 = 15

Thus, simple interest for 5 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 8337.5, then the Principal = ¹⁰⁰/₁₁₅ × 8337.5

= ^{100 × 8337.5}/₁₁₅

= ⁸³³⁷⁵⁰/₁₁₅

= 7250

Thus, Principal = $7250

Thus, the sum borrowed = $7250 Answer

Similar Questions

(1) Jennifer took a loan of $4500 at the rate of 7% simple interest per annum. If he paid an amount of $6390 to clear the loan, then find the time period of the loan.

(2) In how much time a principal of $3150 will amount to $3622.5 at a simple interest of 3% per annum?

(3) Calculate the amount due if Jessica borrowed a sum of $3750 at 3% simple interest for 4 years.

(4) Barbara took a loan of $5100 at the rate of 8% simple interest per annum. If he paid an amount of $8364 to clear the loan, then find the time period of the loan.

(5) If James paid $3360 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(6) Sandra had to pay $5117.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(7) Calculate the amount due if Karen borrowed a sum of $3950 at 3% simple interest for 3 years.

(8) Find the amount to be paid if William borrowed a sum of $5500 at 3% simple interest for 7 years.

(9) 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.

(10) Calculate the amount due after 10 years if Joseph borrowed a sum of $5700 at a rate of 6% simple interest.