Simple Interest
Math MCQs

Question :    How much loan did William borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6600 to clear it?

Correct Answer  $5500

Solution & Explanation

Solution

Given,

Amount (A) = $6600

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

$6600 = P (1 + 4% × 5)

⇒ $6600 = P (1 + ⁴/₁₀₀ × 5)

⇒ $6600 = P (1 + ^{4 × 5}/₁₀₀)

⇒ $6600 = P (1 + ²⁰/₁₀₀)

⇒ $6600 = P (^{100 + 20}/₁₀₀)

⇒ $6600 = P × ¹²⁰/₁₀₀

⇒ P × ¹²⁰/₁₀₀ = $6600

⇒ P = ⁶⁶⁰⁰/_¹²⁰/100

⇒ P = 6600 × ¹⁰⁰/₁₂₀

⇒ P = ^{6600 × 100}/₁₂₀

⇒ P = ⁶⁶⁰⁰⁰⁰/₁₂₀

⇒ 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 = 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 6600, then the Principal = ¹⁰⁰/₁₂₀ × 6600

= ^{100 × 6600}/₁₂₀

= ⁶⁶⁰⁰⁰⁰/₁₂₀

= 5500

Thus, Principal = $5500

Thus, the sum borrowed = $5500 Answer

Similar Questions

(1) How much loan did Donald borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7475 to clear it?

(2) Calculate the amount due after 9 years if Jennifer borrowed a sum of $5250 at a rate of 10% simple interest.

(3) Find the amount to be paid if William borrowed a sum of $5500 at 7% simple interest for 8 years.

(4) Calculate the amount due if Linda borrowed a sum of $3350 at 8% simple interest for 4 years.

(5) Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 7% simple interest.

(6) Calculate the amount due if Karen borrowed a sum of $3950 at 5% simple interest for 3 years.

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

(8) Calculate the amount due if James borrowed a sum of $3000 at 5% simple interest for 4 years.

(9) Mary took a loan of $4100 at the rate of 6% simple interest per annum. If he paid an amount of $5576 to clear the loan, then find the time period of the loan.

(10) David took a loan of $4800 at the rate of 9% simple interest per annum. If he paid an amount of $8256 to clear the loan, then find the time period of the loan.