Simple Interest
Math MCQs

Question :    How much loan did Sharon borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9300 to clear it?

Correct Answer  $7750

Solution & Explanation

Solution

Given,

Amount (A) = $9300

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

$9300 = P (1 + 4% × 5)

⇒ $9300 = P (1 + ⁴/₁₀₀ × 5)

⇒ $9300 = P (1 + ^{4 × 5}/₁₀₀)

⇒ $9300 = P (1 + ²⁰/₁₀₀)

⇒ $9300 = P (^{100 + 20}/₁₀₀)

⇒ $9300 = P × ¹²⁰/₁₀₀

⇒ P × ¹²⁰/₁₀₀ = $9300

⇒ P = ⁹³⁰⁰/_¹²⁰/100

⇒ P = 9300 × ¹⁰⁰/₁₂₀

⇒ P = ^{9300 × 100}/₁₂₀

⇒ P = ⁹³⁰⁰⁰⁰/₁₂₀

⇒ P = $7750

Thus, the sum borrowed (P) = $7750 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 9300, then the Principal = ¹⁰⁰/₁₂₀ × 9300

= ^{100 × 9300}/₁₂₀

= ⁹³⁰⁰⁰⁰/₁₂₀

= 7750

Thus, Principal = $7750

Thus, the sum borrowed = $7750 Answer

Similar Questions

(1) If Betty paid $4930 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(2) Calculate the amount due after 10 years if Barbara borrowed a sum of $5550 at a rate of 3% simple interest.

(3) Donald took a loan of $7000 at the rate of 9% simple interest per annum. If he paid an amount of $12040 to clear the loan, then find the time period of the loan.

(4) How much loan did Carol borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8812.5 to clear it?

(5) Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 4% simple interest.

(6) Calculate the amount due if Charles borrowed a sum of $3900 at 10% simple interest for 3 years.

(7) In how much time a principal of $3050 will amount to $3660 at a simple interest of 5% per annum?

(8) How much loan did George borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9125 to clear it?

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

(10) How much loan did Matthew borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7750 to clear it?