Simple Interest
Math MCQs

Question :    How much loan did Karen borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7437.5 to clear it?

Correct Answer  $5950

Solution & Explanation

Solution

Given,

Amount (A) = $7437.5

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

$7437.5 = P (1 + 5% × 5)

⇒ $7437.5 = P (1 + ⁵/₁₀₀ × 5)

⇒ $7437.5 = P (1 + ^{5 × 5}/₁₀₀)

⇒ $7437.5 = P (1 + ²⁵/₁₀₀)

⇒ $7437.5 = P (^{100 + 25}/₁₀₀)

⇒ $7437.5 = P × ¹²⁵/₁₀₀

⇒ P × ¹²⁵/₁₀₀ = $7437.5

⇒ P = ^7437.5/_¹²⁵/100

⇒ P = 7437.5 × ¹⁰⁰/₁₂₅

⇒ P = ^{7437.5 × 100}/₁₂₅

⇒ P = ⁷⁴³⁷⁵⁰/₁₂₅

⇒ P = $5950

Thus, the sum borrowed (P) = $5950 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 7437.5, then the Principal = ¹⁰⁰/₁₂₅ × 7437.5

= ^{100 × 7437.5}/₁₂₅

= ⁷⁴³⁷⁵⁰/₁₂₅

= 5950

Thus, Principal = $5950

Thus, the sum borrowed = $5950 Answer

Similar Questions

(1) Calculate the amount due if Mary borrowed a sum of $3050 at 9% simple interest for 4 years.

(2) Find the amount to be paid if Charles borrowed a sum of $5900 at 4% simple interest for 8 years.

(3) Calculate the amount due after 9 years if Linda borrowed a sum of $5350 at a rate of 3% simple interest.

(4) Find the amount to be paid if Richard borrowed a sum of $5600 at 9% simple interest for 8 years.

(5) Calculate the amount due if William borrowed a sum of $3500 at 2% simple interest for 3 years.

(6) Betty took a loan of $6500 at the rate of 7% simple interest per annum. If he paid an amount of $10595 to clear the loan, then find the time period of the loan.

(7) Donna had to pay $5286.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(8) How much loan did Daniel borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6710 to clear it?

(9) Find the amount to be paid if Sarah borrowed a sum of $5850 at 10% simple interest for 7 years.

(10) Mary took a loan of $4100 at the rate of 6% simple interest per annum. If he paid an amount of $5576 to clear the loan, then find the time period of the loan.