Simple Interest
Math MCQs

Question :    How much loan did Michael borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6360 to clear it?

Correct Answer  $5300

Solution & Explanation

Solution

Given,

Amount (A) = $6360

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

$6360 = P (1 + 4% × 5)

⇒ $6360 = P (1 + ⁴/₁₀₀ × 5)

⇒ $6360 = P (1 + ^{4 × 5}/₁₀₀)

⇒ $6360 = P (1 + ²⁰/₁₀₀)

⇒ $6360 = P (^{100 + 20}/₁₀₀)

⇒ $6360 = P × ¹²⁰/₁₀₀

⇒ P × ¹²⁰/₁₀₀ = $6360

⇒ P = ⁶³⁶⁰/_¹²⁰/100

⇒ P = 6360 × ¹⁰⁰/₁₂₀

⇒ P = ^{6360 × 100}/₁₂₀

⇒ P = ⁶³⁶⁰⁰⁰/₁₂₀

⇒ P = $5300

Thus, the sum borrowed (P) = $5300 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 6360, then the Principal = ¹⁰⁰/₁₂₀ × 6360

= ^{100 × 6360}/₁₂₀

= ⁶³⁶⁰⁰⁰/₁₂₀

= 5300

Thus, Principal = $5300

Thus, the sum borrowed = $5300 Answer

Similar Questions

(1) Lisa had to pay $4293 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(2) Linda took a loan of $4700 at the rate of 10% simple interest per annum. If he paid an amount of $8460 to clear the loan, then find the time period of the loan.

(3) What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 2% simple interest?

(4) Calculate the amount due after 10 years if Joseph borrowed a sum of $5700 at a rate of 6% simple interest.

(5) How much loan did Stephanie borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8682.5 to clear it?

(6) Nancy took a loan of $6300 at the rate of 7% simple interest per annum. If he paid an amount of $9387 to clear the loan, then find the time period of the loan.

(7) Calculate the amount due if Patricia borrowed a sum of $3150 at 10% simple interest for 3 years.

(8) Joseph took a loan of $5400 at the rate of 6% simple interest per annum. If he paid an amount of $7344 to clear the loan, then find the time period of the loan.

(9) What amount does Jennifer have to pay after 5 years if he takes a loan of $3250 at 9% simple interest?

(10) Calculate the amount due if Jessica borrowed a sum of $3750 at 2% simple interest for 4 years.