Simple Interest
Math MCQs

Question :    How much loan did James borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6250 to clear it?

Correct Answer  $5000

Solution & Explanation

Solution

Given,

Amount (A) = $6250

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

$6250 = P (1 + 5% × 5)

⇒ $6250 = P (1 + ⁵/₁₀₀ × 5)

⇒ $6250 = P (1 + ^{5 × 5}/₁₀₀)

⇒ $6250 = P (1 + ²⁵/₁₀₀)

⇒ $6250 = P (^{100 + 25}/₁₀₀)

⇒ $6250 = P × ¹²⁵/₁₀₀

⇒ P × ¹²⁵/₁₀₀ = $6250

⇒ P = ⁶²⁵⁰/_¹²⁵/100

⇒ P = 6250 × ¹⁰⁰/₁₂₅

⇒ P = ^{6250 × 100}/₁₂₅

⇒ P = ⁶²⁵⁰⁰⁰/₁₂₅

⇒ P = $5000

Thus, the sum borrowed (P) = $5000 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 6250, then the Principal = ¹⁰⁰/₁₂₅ × 6250

= ^{100 × 6250}/₁₂₅

= ⁶²⁵⁰⁰⁰/₁₂₅

= 5000

Thus, Principal = $5000

Thus, the sum borrowed = $5000 Answer

Similar Questions

(1) How much loan did Joseph borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7125 to clear it?

(2) Find the amount to be paid if David borrowed a sum of $5400 at 8% simple interest for 8 years.

(3) Elizabeth took a loan of $4900 at the rate of 8% simple interest per annum. If he paid an amount of $7644 to clear the loan, then find the time period of the loan.

(4) Michael took a loan of $4600 at the rate of 9% simple interest per annum. If he paid an amount of $7084 to clear the loan, then find the time period of the loan.

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

(6) Find the amount to be paid if Richard borrowed a sum of $5600 at 5% simple interest for 7 years.

(7) How much loan did Matthew borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6820 to clear it?

(8) Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 5% simple interest.

(9) Calculate the amount due after 10 years if Thomas borrowed a sum of $5800 at a rate of 3% simple interest.

(10) Matthew took a loan of $6400 at the rate of 7% simple interest per annum. If he paid an amount of $9536 to clear the loan, then find the time period of the loan.