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) In how much time a principal of $3200 will amount to $3328 at a simple interest of 2% per annum?

(2) Calculate the amount due if Sarah borrowed a sum of $3850 at 9% simple interest for 4 years.

(3) If Betty paid $4590 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(4) Joshua had to pay $5194 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(5) Mary had to pay $3233 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(6) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 4% simple interest for 8 years.

(7) Calculate the amount due if Susan borrowed a sum of $3650 at 5% simple interest for 4 years.

(8) If Michael paid $3828 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

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

(10) David took a loan of $4800 at the rate of 9% simple interest per annum. If he paid an amount of $7824 to clear the loan, then find the time period of the loan.