Simple Interest
Math MCQs

Question :    How much loan did Joshua borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8280 to clear it?

Correct Answer  $6900

Solution & Explanation

Solution

Given,

Amount (A) = $8280

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

$8280 = P (1 + 4% × 5)

⇒ $8280 = P (1 + ⁴/₁₀₀ × 5)

⇒ $8280 = P (1 + ^{4 × 5}/₁₀₀)

⇒ $8280 = P (1 + ²⁰/₁₀₀)

⇒ $8280 = P (^{100 + 20}/₁₀₀)

⇒ $8280 = P × ¹²⁰/₁₀₀

⇒ P × ¹²⁰/₁₀₀ = $8280

⇒ P = ⁸²⁸⁰/_¹²⁰/100

⇒ P = 8280 × ¹⁰⁰/₁₂₀

⇒ P = ^{8280 × 100}/₁₂₀

⇒ P = ⁸²⁸⁰⁰⁰/₁₂₀

⇒ P = $6900

Thus, the sum borrowed (P) = $6900 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 8280, then the Principal = ¹⁰⁰/₁₂₀ × 8280

= ^{100 × 8280}/₁₂₀

= ⁸²⁸⁰⁰⁰/₁₂₀

= 6900

Thus, Principal = $6900

Thus, the sum borrowed = $6900 Answer

Similar Questions

(1) Find the amount to be paid if William borrowed a sum of $5500 at 5% simple interest for 8 years.

(2) Calculate the amount due if Mary borrowed a sum of $3050 at 3% simple interest for 3 years.

(3) Calculate the amount due after 10 years if Susan borrowed a sum of $5650 at a rate of 7% simple interest.

(4) Find the amount to be paid if James borrowed a sum of $5000 at 7% simple interest for 7 years.

(5) How much loan did Sandra borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7095 to clear it?

(6) David took a loan of $4800 at the rate of 8% simple interest per annum. If he paid an amount of $8256 to clear the loan, then find the time period of the loan.

(7) Find the amount to be paid if William borrowed a sum of $5500 at 2% simple interest for 7 years.

(8) Calculate the amount due after 9 years if Thomas borrowed a sum of $5800 at a rate of 2% simple interest.

(9) In how much time a principal of $3050 will amount to $3507.5 at a simple interest of 5% per annum?

(10) Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 10% simple interest.