Simple Interest
Math MCQs

Question :    How much loan did Thomas borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6960 to clear it?

Correct Answer  $5800

Solution & Explanation

Solution

Given,

Amount (A) = $6960

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

$6960 = P (1 + 4% × 5)

⇒ $6960 = P (1 + ⁴/₁₀₀ × 5)

⇒ $6960 = P (1 + ^{4 × 5}/₁₀₀)

⇒ $6960 = P (1 + ²⁰/₁₀₀)

⇒ $6960 = P (^{100 + 20}/₁₀₀)

⇒ $6960 = P × ¹²⁰/₁₀₀

⇒ P × ¹²⁰/₁₀₀ = $6960

⇒ P = ⁶⁹⁶⁰/_¹²⁰/100

⇒ P = 6960 × ¹⁰⁰/₁₂₀

⇒ P = ^{6960 × 100}/₁₂₀

⇒ P = ⁶⁹⁶⁰⁰⁰/₁₂₀

⇒ P = $5800

Thus, the sum borrowed (P) = $5800 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 6960, then the Principal = ¹⁰⁰/₁₂₀ × 6960

= ^{100 × 6960}/₁₂₀

= ⁶⁹⁶⁰⁰⁰/₁₂₀

= 5800

Thus, Principal = $5800

Thus, the sum borrowed = $5800 Answer

Similar Questions

(1) Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 10% simple interest.

(2) 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.

(3) If Susan paid $3942 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(4) Calculate the amount due if Mary borrowed a sum of $3050 at 10% simple interest for 3 years.

(5) Find the amount to be paid if Robert borrowed a sum of $5100 at 8% simple interest for 7 years.

(6) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 2% simple interest for 3 years.

(7) Joseph took a loan of $5400 at the rate of 7% simple interest per annum. If he paid an amount of $8424 to clear the loan, then find the time period of the loan.

(8) Calculate the amount due if Barbara borrowed a sum of $3550 at 6% simple interest for 3 years.

(9) How much loan did Kevin borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8875 to clear it?

(10) How much loan did Dorothy borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8700 to clear it?