Simple Interest
Math MCQs

Question :    How much loan did Andrew borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8160 to clear it?

Correct Answer  $6800

Solution & Explanation

Solution

Given,

Amount (A) = $8160

Rate of Simple Interest (R) = 4%

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

$8160 = P (1 + 4% × 5)

⇒ $8160 = P (1 + ⁴/₁₀₀ × 5)

⇒ $8160 = P (1 + ^{4 × 5}/₁₀₀)

⇒ $8160 = P (1 + ²⁰/₁₀₀)

⇒ $8160 = P (^{100 + 20}/₁₀₀)

⇒ $8160 = P × ¹²⁰/₁₀₀

⇒ P × ¹²⁰/₁₀₀ = $8160

⇒ P = ⁸¹⁶⁰/_¹²⁰/100

⇒ P = 8160 × ¹⁰⁰/₁₂₀

⇒ P = ^{8160 × 100}/₁₂₀

⇒ P = ⁸¹⁶⁰⁰⁰/₁₂₀

⇒ P = $6800

Thus, the sum borrowed (P) = $6800 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 = 4% per annum

Thus, Interest = 4% of principal

⇒ Interest = 4% of 100 = 4

Thus, Simple Interest for 1 year = 4

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 × 4 = 20

Thus, simple interest for 5 years = 20

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 20 = 120

Calculation of the Principal

Now,

∵ If the Amount is 120, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₂₀

∴ If the Amount is 8160, then the Principal = ¹⁰⁰/₁₂₀ × 8160

= ^{100 × 8160}/₁₂₀

= ⁸¹⁶⁰⁰⁰/₁₂₀

= 6800

Thus, Principal = $6800

Thus, the sum borrowed = $6800 Answer

Similar Questions

(1) Calculate the amount due if David borrowed a sum of $3400 at 3% simple interest for 4 years.

(2) Thomas took a loan of $5600 at the rate of 8% simple interest per annum. If he paid an amount of $10080 to clear the loan, then find the time period of the loan.

(3) Robert took a loan of $4200 at the rate of 10% simple interest per annum. If he paid an amount of $6720 to clear the loan, then find the time period of the loan.

(4) Calculate the amount due if Michael borrowed a sum of $3300 at 10% simple interest for 3 years.

(5) Calculate the amount due if James borrowed a sum of $3000 at 10% simple interest for 3 years.

(6) Robert took a loan of $4200 at the rate of 9% simple interest per annum. If he paid an amount of $7224 to clear the loan, then find the time period of the loan.

(7) How much loan did David borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5940 to clear it?

(8) Elizabeth took a loan of $4900 at the rate of 7% simple interest per annum. If he paid an amount of $7301 to clear the loan, then find the time period of the loan.

(9) What amount will be due after 2 years if Robert borrowed a sum of $3050 at a 8% simple interest?

(10) What amount does James have to pay after 6 years if he takes a loan of $3000 at 3% simple interest?