Simple Interest
Math MCQs

Question :    How much loan did Joseph borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6840 to clear it?

Correct Answer  $5700

Solution & Explanation

Solution

Given,

Amount (A) = $6840

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

$6840 = P (1 + 4% × 5)

⇒ $6840 = P (1 + ⁴/₁₀₀ × 5)

⇒ $6840 = P (1 + ^{4 × 5}/₁₀₀)

⇒ $6840 = P (1 + ²⁰/₁₀₀)

⇒ $6840 = P (^{100 + 20}/₁₀₀)

⇒ $6840 = P × ¹²⁰/₁₀₀

⇒ P × ¹²⁰/₁₀₀ = $6840

⇒ P = ⁶⁸⁴⁰/_¹²⁰/100

⇒ P = 6840 × ¹⁰⁰/₁₂₀

⇒ P = ^{6840 × 100}/₁₂₀

⇒ P = ⁶⁸⁴⁰⁰⁰/₁₂₀

⇒ P = $5700

Thus, the sum borrowed (P) = $5700 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 6840, then the Principal = ¹⁰⁰/₁₂₀ × 6840

= ^{100 × 6840}/₁₂₀

= ⁶⁸⁴⁰⁰⁰/₁₂₀

= 5700

Thus, Principal = $5700

Thus, the sum borrowed = $5700 Answer

Similar Questions

(1) Find the amount to be paid if Patricia borrowed a sum of $5150 at 2% simple interest for 8 years.

(2) What amount does Karen have to pay after 5 years if he takes a loan of $3950 at 8% simple interest?

(3) Find the amount to be paid if Barbara borrowed a sum of $5550 at 5% simple interest for 8 years.

(4) Jennifer took a loan of $4500 at the rate of 6% simple interest per annum. If he paid an amount of $6930 to clear the loan, then find the time period of the loan.

(5) Michael took a loan of $4600 at the rate of 8% simple interest per annum. If he paid an amount of $7544 to clear the loan, then find the time period of the loan.

(6) Linda took a loan of $4700 at the rate of 8% simple interest per annum. If he paid an amount of $7332 to clear the loan, then find the time period of the loan.

(7) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 5% simple interest for 8 years.

(8) Susan took a loan of $5300 at the rate of 9% simple interest per annum. If he paid an amount of $9593 to clear the loan, then find the time period of the loan.

(9) Calculate the amount due if Patricia borrowed a sum of $3150 at 8% simple interest for 3 years.

(10) How much loan did William borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6325 to clear it?