Simple Interest
Math MCQs

Question :    How much loan did Karen borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7140 to clear it?

Correct Answer  $5950

Solution & Explanation

Solution

Given,

Amount (A) = $7140

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

$7140 = P (1 + 4% × 5)

⇒ $7140 = P (1 + ⁴/₁₀₀ × 5)

⇒ $7140 = P (1 + ^{4 × 5}/₁₀₀)

⇒ $7140 = P (1 + ²⁰/₁₀₀)

⇒ $7140 = P (^{100 + 20}/₁₀₀)

⇒ $7140 = P × ¹²⁰/₁₀₀

⇒ P × ¹²⁰/₁₀₀ = $7140

⇒ P = ⁷¹⁴⁰/_¹²⁰/100

⇒ P = 7140 × ¹⁰⁰/₁₂₀

⇒ P = ^{7140 × 100}/₁₂₀

⇒ P = ⁷¹⁴⁰⁰⁰/₁₂₀

⇒ P = $5950

Thus, the sum borrowed (P) = $5950 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 7140, then the Principal = ¹⁰⁰/₁₂₀ × 7140

= ^{100 × 7140}/₁₂₀

= ⁷¹⁴⁰⁰⁰/₁₂₀

= 5950

Thus, Principal = $5950

Thus, the sum borrowed = $5950 Answer

Similar Questions

(1) Nancy had to pay $4772.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(2) James had to pay $3360 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(3) How much loan did Brian borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7920 to clear it?

(4) Linda took a loan of $4700 at the rate of 7% simple interest per annum. If he paid an amount of $7332 to clear the loan, then find the time period of the loan.

(5) Thomas had to pay $4256 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(6) Find the amount to be paid if Thomas borrowed a sum of $5800 at 4% simple interest for 8 years.

(7) How much loan did Jeffrey borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9360 to clear it?

(8) In how much time a principal of $3050 will amount to $3355 at a simple interest of 2% per annum?

(9) What amount does James have to pay after 6 years if he takes a loan of $3000 at 10% simple interest?

(10) Find the amount to be paid if Jessica borrowed a sum of $5750 at 10% simple interest for 8 years.