Simple Interest
Math MCQs

Question :    How much loan did Robert borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6120 to clear it?

Correct Answer  $5100

Solution & Explanation

Solution

Given,

Amount (A) = $6120

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

$6120 = P (1 + 4% × 5)

⇒ $6120 = P (1 + ⁴/₁₀₀ × 5)

⇒ $6120 = P (1 + ^{4 × 5}/₁₀₀)

⇒ $6120 = P (1 + ²⁰/₁₀₀)

⇒ $6120 = P (^{100 + 20}/₁₀₀)

⇒ $6120 = P × ¹²⁰/₁₀₀

⇒ P × ¹²⁰/₁₀₀ = $6120

⇒ P = ⁶¹²⁰/_¹²⁰/100

⇒ P = 6120 × ¹⁰⁰/₁₂₀

⇒ P = ^{6120 × 100}/₁₂₀

⇒ P = ⁶¹²⁰⁰⁰/₁₂₀

⇒ P = $5100

Thus, the sum borrowed (P) = $5100 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 6120, then the Principal = ¹⁰⁰/₁₂₀ × 6120

= ^{100 × 6120}/₁₂₀

= ⁶¹²⁰⁰⁰/₁₂₀

= 5100

Thus, Principal = $5100

Thus, the sum borrowed = $5100 Answer

Similar Questions

(1) What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 10% simple interest?

(2) Calculate the amount due if William borrowed a sum of $3500 at 8% simple interest for 3 years.

(3) Jennifer took a loan of $4500 at the rate of 6% simple interest per annum. If he paid an amount of $6660 to clear the loan, then find the time period of the loan.

(4) Susan took a loan of $5300 at the rate of 8% simple interest per annum. If he paid an amount of $9540 to clear the loan, then find the time period of the loan.

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

(6) What amount will be due after 2 years if Paul borrowed a sum of $3850 at a 8% simple interest?

(7) Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 4% simple interest.

(8) Sarah took a loan of $5700 at the rate of 7% simple interest per annum. If he paid an amount of $8094 to clear the loan, then find the time period of the loan.

(9) Find the amount to be paid if David borrowed a sum of $5400 at 10% simple interest for 8 years.

(10) Calculate the amount due if Richard borrowed a sum of $3600 at 2% simple interest for 3 years.