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) Calculate the amount due if Jessica borrowed a sum of $3750 at 6% simple interest for 3 years.

(2) Calculate the amount due if David borrowed a sum of $3400 at 7% simple interest for 3 years.

(3) Calculate the amount due if Thomas borrowed a sum of $3800 at 4% simple interest for 4 years.

(4) Find the amount to be paid if Linda borrowed a sum of $5350 at 10% simple interest for 8 years.

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

(6) Anthony took a loan of $6600 at the rate of 8% simple interest per annum. If he paid an amount of $9768 to clear the loan, then find the time period of the loan.

(7) Calculate the amount due if Karen borrowed a sum of $3950 at 9% simple interest for 3 years.

(8) Christopher had to pay $4600 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(9) Jessica took a loan of $5500 at the rate of 9% simple interest per annum. If he paid an amount of $8965 to clear the loan, then find the time period of the loan.

(10) Find the amount to be paid if Patricia borrowed a sum of $5150 at 8% simple interest for 8 years.