Simple Interest
Math MCQs

Question :    How much loan did Paul borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8040 to clear it?

Correct Answer  $6700

Solution & Explanation

Solution

Given,

Amount (A) = $8040

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

$8040 = P (1 + 4% × 5)

⇒ $8040 = P (1 + ⁴/₁₀₀ × 5)

⇒ $8040 = P (1 + ^{4 × 5}/₁₀₀)

⇒ $8040 = P (1 + ²⁰/₁₀₀)

⇒ $8040 = P (^{100 + 20}/₁₀₀)

⇒ $8040 = P × ¹²⁰/₁₀₀

⇒ P × ¹²⁰/₁₀₀ = $8040

⇒ P = ⁸⁰⁴⁰/_¹²⁰/100

⇒ P = 8040 × ¹⁰⁰/₁₂₀

⇒ P = ^{8040 × 100}/₁₂₀

⇒ P = ⁸⁰⁴⁰⁰⁰/₁₂₀

⇒ P = $6700

Thus, the sum borrowed (P) = $6700 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 8040, then the Principal = ¹⁰⁰/₁₂₀ × 8040

= ^{100 × 8040}/₁₂₀

= ⁸⁰⁴⁰⁰⁰/₁₂₀

= 6700

Thus, Principal = $6700

Thus, the sum borrowed = $6700 Answer

Similar Questions

(1) Calculate the amount due after 9 years if Thomas borrowed a sum of $5800 at a rate of 3% simple interest.

(2) Jennifer took a loan of $4500 at the rate of 8% simple interest per annum. If he paid an amount of $8100 to clear the loan, then find the time period of the loan.

(3) In how much time a principal of $3100 will amount to $3596 at a simple interest of 4% per annum?

(4) Barbara took a loan of $5100 at the rate of 8% simple interest per annum. If he paid an amount of $7956 to clear the loan, then find the time period of the loan.

(5) Calculate the amount due after 10 years if Mary borrowed a sum of $5050 at a rate of 5% simple interest.

(6) Sarah had to pay $4427.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(7) If Patricia borrowed $3150 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.

(8) What amount does Richard have to pay after 5 years if he takes a loan of $3600 at 2% simple interest?

(9) How much loan did Margaret borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7620 to clear it?

(10) Calculate the amount due if Christopher borrowed a sum of $4000 at 2% simple interest for 3 years.