Simple Interest
Math MCQs

Question :    How much loan did Mark borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8000 to clear it?

Correct Answer  $6400

Solution & Explanation

Solution

Given,

Amount (A) = $8000

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

$8000 = P (1 + 5% × 5)

⇒ $8000 = P (1 + ⁵/₁₀₀ × 5)

⇒ $8000 = P (1 + ^{5 × 5}/₁₀₀)

⇒ $8000 = P (1 + ²⁵/₁₀₀)

⇒ $8000 = P (^{100 + 25}/₁₀₀)

⇒ $8000 = P × ¹²⁵/₁₀₀

⇒ P × ¹²⁵/₁₀₀ = $8000

⇒ P = ⁸⁰⁰⁰/_¹²⁵/100

⇒ P = 8000 × ¹⁰⁰/₁₂₅

⇒ P = ^{8000 × 100}/₁₂₅

⇒ P = ⁸⁰⁰⁰⁰⁰/₁₂₅

⇒ P = $6400

Thus, the sum borrowed (P) = $6400 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 8000, then the Principal = ¹⁰⁰/₁₂₅ × 8000

= ^{100 × 8000}/₁₂₅

= ⁸⁰⁰⁰⁰⁰/₁₂₅

= 6400

Thus, Principal = $6400

Thus, the sum borrowed = $6400 Answer

Similar Questions

(1) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 7% simple interest for 8 years.

(2) Jessica took a loan of $5500 at the rate of 7% simple interest per annum. If he paid an amount of $7810 to clear the loan, then find the time period of the loan.

(3) Christopher took a loan of $6000 at the rate of 7% simple interest per annum. If he paid an amount of $8940 to clear the loan, then find the time period of the loan.

(4) Calculate the amount due if Susan borrowed a sum of $3650 at 10% simple interest for 3 years.

(5) Jennifer took a loan of $4500 at the rate of 9% simple interest per annum. If he paid an amount of $8550 to clear the loan, then find the time period of the loan.

(6) Calculate the amount due if Barbara borrowed a sum of $3550 at 7% simple interest for 3 years.

(7) William took a loan of $5000 at the rate of 6% simple interest per annum. If he paid an amount of $7400 to clear the loan, then find the time period of the loan.

(8) Anthony took a loan of $6600 at the rate of 10% simple interest per annum. If he paid an amount of $13200 to clear the loan, then find the time period of the loan.

(9) Donald took a loan of $7000 at the rate of 10% simple interest per annum. If he paid an amount of $11200 to clear the loan, then find the time period of the loan.

(10) Nancy took a loan of $6300 at the rate of 10% simple interest per annum. If he paid an amount of $12600 to clear the loan, then find the time period of the loan.