Simple Interest
Math MCQs

Question :    How much loan did Donna borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7535 to clear it?

Correct Answer  $6850

Solution & Explanation

Solution

Given,

Amount (A) = $7535

Rate of Simple Interest (R) = 2%

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

$7535 = P (1 + 2% × 5)

⇒ $7535 = P (1 + ²/₁₀₀ × 5)

⇒ $7535 = P (1 + ^{2 × 5}/₁₀₀)

⇒ $7535 = P (1 + ¹⁰/₁₀₀)

⇒ $7535 = P (^{100 + 10}/₁₀₀)

⇒ $7535 = P × ¹¹⁰/₁₀₀

⇒ P × ¹¹⁰/₁₀₀ = $7535

⇒ P = ⁷⁵³⁵/_¹¹⁰/100

⇒ P = 7535 × ¹⁰⁰/₁₁₀

⇒ P = ^{7535 × 100}/₁₁₀

⇒ P = ⁷⁵³⁵⁰⁰/₁₁₀

⇒ P = $6850

Thus, the sum borrowed (P) = $6850 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 = 2% per annum

Thus, Interest = 2% of principal

⇒ Interest = 2% of 100 = 2

Thus, Simple Interest for 1 year = 2

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 × 2 = 10

Thus, simple interest for 5 years = 10

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 10 = 110

Calculation of the Principal

Now,

∵ If the Amount is 110, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₁₀

∴ If the Amount is 7535, then the Principal = ¹⁰⁰/₁₁₀ × 7535

= ^{100 × 7535}/₁₁₀

= ⁷⁵³⁵⁰⁰/₁₁₀

= 6850

Thus, Principal = $6850

Thus, the sum borrowed = $6850 Answer

Similar Questions

(1) Find the amount to be paid if Christopher borrowed a sum of $6000 at 9% simple interest for 8 years.

(2) Sarah took a loan of $5700 at the rate of 7% simple interest per annum. If he paid an amount of $8094 to clear the loan, then find the time period of the loan.

(3) Sandra took a loan of $6900 at the rate of 9% simple interest per annum. If he paid an amount of $11868 to clear the loan, then find the time period of the loan.

(4) Find the amount to be paid if Jessica borrowed a sum of $5750 at 2% simple interest for 7 years.

(5) What amount does Michael have to pay after 5 years if he takes a loan of $3300 at 10% simple interest?

(6) Find the amount to be paid if James borrowed a sum of $5000 at 4% simple interest for 7 years.

(7) William took a loan of $5000 at the rate of 9% simple interest per annum. If he paid an amount of $8150 to clear the loan, then find the time period of the loan.

(8) Mark took a loan of $6800 at the rate of 6% simple interest per annum. If he paid an amount of $10472 to clear the loan, then find the time period of the loan.

(9) Calculate the amount due if Sarah borrowed a sum of $3850 at 5% simple interest for 3 years.

(10) William took a loan of $5000 at the rate of 6% simple interest per annum. If he paid an amount of $6800 to clear the loan, then find the time period of the loan.