Simple Interest
Math MCQs

Question :    How much loan did William borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6050 to clear it?

Correct Answer  $5500

Solution & Explanation

Solution

Given,

Amount (A) = $6050

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

$6050 = P (1 + 2% × 5)

⇒ $6050 = P (1 + ²/₁₀₀ × 5)

⇒ $6050 = P (1 + ^{2 × 5}/₁₀₀)

⇒ $6050 = P (1 + ¹⁰/₁₀₀)

⇒ $6050 = P (^{100 + 10}/₁₀₀)

⇒ $6050 = P × ¹¹⁰/₁₀₀

⇒ P × ¹¹⁰/₁₀₀ = $6050

⇒ P = ⁶⁰⁵⁰/_¹¹⁰/100

⇒ P = 6050 × ¹⁰⁰/₁₁₀

⇒ P = ^{6050 × 100}/₁₁₀

⇒ P = ⁶⁰⁵⁰⁰⁰/₁₁₀

⇒ P = $5500

Thus, the sum borrowed (P) = $5500 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 6050, then the Principal = ¹⁰⁰/₁₁₀ × 6050

= ^{100 × 6050}/₁₁₀

= ⁶⁰⁵⁰⁰⁰/₁₁₀

= 5500

Thus, Principal = $5500

Thus, the sum borrowed = $5500 Answer

Similar Questions

(1) James took a loan of $4000 at the rate of 7% simple interest per annum. If he paid an amount of $5680 to clear the loan, then find the time period of the loan.

(2) William took a loan of $5000 at the rate of 10% simple interest per annum. If he paid an amount of $9000 to clear the loan, then find the time period of the loan.

(3) Find the amount to be paid if Thomas borrowed a sum of $5800 at 9% simple interest for 7 years.

(4) David took a loan of $4800 at the rate of 7% simple interest per annum. If he paid an amount of $7824 to clear the loan, then find the time period of the loan.

(5) How much loan did Laura borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8635 to clear it?

(6) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 10% simple interest for 8 years.

(7) What amount does Mary have to pay after 5 years if he takes a loan of $3050 at 10% simple interest?

(8) What amount will be due after 2 years if Mark borrowed a sum of $3700 at a 5% simple interest?

(9) Richard took a loan of $5200 at the rate of 6% simple interest per annum. If he paid an amount of $7072 to clear the loan, then find the time period of the loan.

(10) Calculate the amount due after 10 years if Robert borrowed a sum of $5100 at a rate of 7% simple interest.