Simple Interest
Math MCQs

Question :    How much loan did Paul borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8375 to clear it?

Correct Answer  $6700

Solution & Explanation

Solution

Given,

Amount (A) = $8375

Rate of Simple Interest (R) = 5%

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

$8375 = P (1 + 5% × 5)

⇒ $8375 = P (1 + ⁵/₁₀₀ × 5)

⇒ $8375 = P (1 + ^{5 × 5}/₁₀₀)

⇒ $8375 = P (1 + ²⁵/₁₀₀)

⇒ $8375 = P (^{100 + 25}/₁₀₀)

⇒ $8375 = P × ¹²⁵/₁₀₀

⇒ P × ¹²⁵/₁₀₀ = $8375

⇒ P = ⁸³⁷⁵/_¹²⁵/100

⇒ P = 8375 × ¹⁰⁰/₁₂₅

⇒ P = ^{8375 × 100}/₁₂₅

⇒ P = ⁸³⁷⁵⁰⁰/₁₂₅

⇒ P = $6700

Thus, the sum borrowed (P) = $6700 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 = 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 × 5 = 25

Thus, simple interest for 5 years = 25

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 25 = 125

Calculation of the Principal

Now,

∵ If the Amount is 125, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₂₅

∴ If the Amount is 8375, then the Principal = ¹⁰⁰/₁₂₅ × 8375

= ^{100 × 8375}/₁₂₅

= ⁸³⁷⁵⁰⁰/₁₂₅

= 6700

Thus, Principal = $6700

Thus, the sum borrowed = $6700 Answer

Similar Questions

(1) Barbara took a loan of $5100 at the rate of 7% simple interest per annum. If he paid an amount of $7242 to clear the loan, then find the time period of the loan.

(2) How much loan did Andrew borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7820 to clear it?

(3) In how much time a principal of $3050 will amount to $3538 at a simple interest of 4% per annum?

(4) Christopher had to pay $4480 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(5) Donna had to pay $5577.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(6) Find the amount to be paid if John borrowed a sum of $5200 at 3% simple interest for 8 years.

(7) Joshua had to pay $5341 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(8) Calculate the amount due if James borrowed a sum of $3000 at 5% simple interest for 4 years.

(9) Calculate the amount due if Thomas borrowed a sum of $3800 at 8% simple interest for 3 years.

(10) If Emily paid $5130 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.