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) Elizabeth took a loan of $4900 at the rate of 10% simple interest per annum. If he paid an amount of $9800 to clear the loan, then find the time period of the loan.

(2) Jessica took a loan of $5500 at the rate of 9% simple interest per annum. If he paid an amount of $8965 to clear the loan, then find the time period of the loan.

(3) Sandra took a loan of $6900 at the rate of 10% simple interest per annum. If he paid an amount of $11040 to clear the loan, then find the time period of the loan.

(4) Patricia took a loan of $4300 at the rate of 10% simple interest per annum. If he paid an amount of $7740 to clear the loan, then find the time period of the loan.

(5) Calculate the amount due after 10 years if Jessica borrowed a sum of $5750 at a rate of 2% simple interest.

(6) Mary had to pay $3416 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(7) Calculate the amount due after 9 years if John borrowed a sum of $5200 at a rate of 5% simple interest.

(8) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 9% simple interest for 8 years.

(9) How much loan did Jacob borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9600 to clear it?

(10) What amount does Richard have to pay after 5 years if he takes a loan of $3600 at 2% simple interest?