Simple Interest
Math MCQs

Question :  ( 1 of 10 )  How much loan did James borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5500 to clear it?

Correct Answer  $5000

Solution & Explanation

Solution

Given,

Amount (A) = $5500

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

$5500 = P (1 + 2% × 5)

⇒ $5500 = P (1 + ²/₁₀₀ × 5)

⇒ $5500 = P (1 + ^{2 × 5}/₁₀₀)

⇒ $5500 = P (1 + ¹⁰/₁₀₀)

⇒ $5500 = P (^{100 + 10}/₁₀₀)

⇒ $5500 = P × ¹¹⁰/₁₀₀

⇒ P × ¹¹⁰/₁₀₀ = $5500

⇒ P = ⁵⁵⁰⁰/_¹¹⁰/100

⇒ P = 5500 × ¹⁰⁰/₁₁₀

⇒ P = ^{5500 × 100}/₁₁₀

⇒ P = ⁵⁵⁰⁰⁰⁰/₁₁₀

⇒ 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 = 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 5500, then the Principal = ¹⁰⁰/₁₁₀ × 5500

= ^{100 × 5500}/₁₁₀

= ⁵⁵⁰⁰⁰⁰/₁₁₀

= 5000

Thus, Principal = $5000

Thus, the sum borrowed = $5000 Answer

Similar Questions

(1) Linda took a loan of $4700 at the rate of 8% simple interest per annum. If he paid an amount of $8084 to clear the loan, then find the time period of the loan.

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

(3) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 3% simple interest?

(4) How much loan did Elizabeth borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5995 to clear it?

(5) Calculate the amount due if Jessica borrowed a sum of $3750 at 10% simple interest for 4 years.

(6) John took a loan of $4400 at the rate of 6% simple interest per annum. If he paid an amount of $7040 to clear the loan, then find the time period of the loan.

(7) Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 4% simple interest.

(8) Sandra took a loan of $6900 at the rate of 6% simple interest per annum. If he paid an amount of $10626 to clear the loan, then find the time period of the loan.

(9) Find the amount to be paid if Joseph borrowed a sum of $5700 at 2% simple interest for 7 years.

(10) Steven had to pay $5014 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.