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) Robert took a loan of $4200 at the rate of 6% simple interest per annum. If he paid an amount of $5712 to clear the loan, then find the time period of the loan.

(2) Karen had to pay $4305.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(3) Calculate the amount due if David borrowed a sum of $3400 at 7% simple interest for 3 years.

(4) How much loan did Mary borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5555 to clear it?

(5) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 4% simple interest for 4 years.

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

(7) Calculate the amount due if Linda borrowed a sum of $3350 at 7% simple interest for 3 years.

(8) Calculate the amount due if Michael borrowed a sum of $3300 at 2% simple interest for 3 years.

(9) Karen took a loan of $5900 at the rate of 9% simple interest per annum. If he paid an amount of $11210 to clear the loan, then find the time period of the loan.

(10) Calculate the amount due if David borrowed a sum of $3400 at 9% simple interest for 3 years.