Simple Interest
Math MCQs

Question :    How much loan did Christopher borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6600 to clear it?

Correct Answer  $6000

Solution & Explanation

Solution

Given,

Amount (A) = $6600

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

$6600 = P (1 + 2% × 5)

⇒ $6600 = P (1 + ²/₁₀₀ × 5)

⇒ $6600 = P (1 + ^{2 × 5}/₁₀₀)

⇒ $6600 = P (1 + ¹⁰/₁₀₀)

⇒ $6600 = P (^{100 + 10}/₁₀₀)

⇒ $6600 = P × ¹¹⁰/₁₀₀

⇒ P × ¹¹⁰/₁₀₀ = $6600

⇒ P = ⁶⁶⁰⁰/_¹¹⁰/100

⇒ P = 6600 × ¹⁰⁰/₁₁₀

⇒ P = ^{6600 × 100}/₁₁₀

⇒ P = ⁶⁶⁰⁰⁰⁰/₁₁₀

⇒ P = $6000

Thus, the sum borrowed (P) = $6000 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 6600, then the Principal = ¹⁰⁰/₁₁₀ × 6600

= ^{100 × 6600}/₁₁₀

= ⁶⁶⁰⁰⁰⁰/₁₁₀

= 6000

Thus, Principal = $6000

Thus, the sum borrowed = $6000 Answer

Similar Questions

(1) How much loan did Andrew borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8500 to clear it?

(2) Matthew took a loan of $6400 at the rate of 7% simple interest per annum. If he paid an amount of $10432 to clear the loan, then find the time period of the loan.

(3) Anthony took a loan of $6600 at the rate of 6% simple interest per annum. If he paid an amount of $9768 to clear the loan, then find the time period of the loan.

(4) How much loan did James borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6250 to clear it?

(5) Donald had to pay $5040 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(6) Calculate the amount due if John borrowed a sum of $3200 at 7% simple interest for 4 years.

(7) Patricia took a loan of $4300 at the rate of 6% simple interest per annum. If he paid an amount of $6106 to clear the loan, then find the time period of the loan.

(8) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 5% simple interest?

(9) Find the amount to be paid if Karen borrowed a sum of $5950 at 7% simple interest for 8 years.

(10) Calculate the amount due if David borrowed a sum of $3400 at 7% simple interest for 4 years.