Simple Interest
Math MCQs

Question :    How much loan did Kenneth borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8750 to clear it?

Correct Answer  $7000

Solution & Explanation

Solution

Given,

Amount (A) = $8750

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

$8750 = P (1 + 5% × 5)

⇒ $8750 = P (1 + ⁵/₁₀₀ × 5)

⇒ $8750 = P (1 + ^{5 × 5}/₁₀₀)

⇒ $8750 = P (1 + ²⁵/₁₀₀)

⇒ $8750 = P (^{100 + 25}/₁₀₀)

⇒ $8750 = P × ¹²⁵/₁₀₀

⇒ P × ¹²⁵/₁₀₀ = $8750

⇒ P = ⁸⁷⁵⁰/_¹²⁵/100

⇒ P = 8750 × ¹⁰⁰/₁₂₅

⇒ P = ^{8750 × 100}/₁₂₅

⇒ P = ⁸⁷⁵⁰⁰⁰/₁₂₅

⇒ P = $7000

Thus, the sum borrowed (P) = $7000 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 8750, then the Principal = ¹⁰⁰/₁₂₅ × 8750

= ^{100 × 8750}/₁₂₅

= ⁸⁷⁵⁰⁰⁰/₁₂₅

= 7000

Thus, Principal = $7000

Thus, the sum borrowed = $7000 Answer

Similar Questions

(1) Sandra took a loan of $6900 at the rate of 7% simple interest per annum. If he paid an amount of $10281 to clear the loan, then find the time period of the loan.

(2) Find the amount to be paid if Jessica borrowed a sum of $5750 at 4% simple interest for 8 years.

(3) In how much time a principal of $3100 will amount to $3596 at a simple interest of 4% per annum?

(4) Jessica had to pay $4087.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(5) How much loan did Timothy borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8510 to clear it?

(6) Calculate the amount due after 9 years if Charles borrowed a sum of $5900 at a rate of 10% simple interest.

(7) How much loan did Jacob borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $9200 to clear it?

(8) Calculate the amount due if Jennifer borrowed a sum of $3250 at 10% simple interest for 4 years.

(9) 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.

(10) Find the amount to be paid if Susan borrowed a sum of $5650 at 6% simple interest for 7 years.