Simple Interest
Math MCQs

Question :    How much loan did Cynthia borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8745 to clear it?

Correct Answer  $7950

Solution & Explanation

Solution

Given,

Amount (A) = $8745

Rate of Simple Interest (R) = 2%

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

$8745 = P (1 + 2% × 5)

⇒ $8745 = P (1 + ²/₁₀₀ × 5)

⇒ $8745 = P (1 + ^{2 × 5}/₁₀₀)

⇒ $8745 = P (1 + ¹⁰/₁₀₀)

⇒ $8745 = P (^{100 + 10}/₁₀₀)

⇒ $8745 = P × ¹¹⁰/₁₀₀

⇒ P × ¹¹⁰/₁₀₀ = $8745

⇒ P = ⁸⁷⁴⁵/_¹¹⁰/100

⇒ P = 8745 × ¹⁰⁰/₁₁₀

⇒ P = ^{8745 × 100}/₁₁₀

⇒ P = ⁸⁷⁴⁵⁰⁰/₁₁₀

⇒ P = $7950

Thus, the sum borrowed (P) = $7950 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 = 2% per annum

Thus, Interest = 2% of principal

⇒ Interest = 2% of 100 = 2

Thus, Simple Interest for 1 year = 2

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 × 2 = 10

Thus, simple interest for 5 years = 10

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 10 = 110

Calculation of the Principal

Now,

∵ If the Amount is 110, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₁₀

∴ If the Amount is 8745, then the Principal = ¹⁰⁰/₁₁₀ × 8745

= ^{100 × 8745}/₁₁₀

= ⁸⁷⁴⁵⁰⁰/₁₁₀

= 7950

Thus, Principal = $7950

Thus, the sum borrowed = $7950 Answer

Similar Questions

(1) Calculate the amount due if Robert borrowed a sum of $3100 at 3% simple interest for 3 years.

(2) Calculate the amount due after 9 years if Robert borrowed a sum of $5100 at a rate of 8% simple interest.

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

(4) What amount does Elizabeth have to pay after 6 years if he takes a loan of $3450 at 9% simple interest?

(5) Christopher took a loan of $6000 at the rate of 9% simple interest per annum. If he paid an amount of $9240 to clear the loan, then find the time period of the loan.

(6) Find the amount to be paid if William borrowed a sum of $5500 at 8% simple interest for 7 years.

(7) What amount will be due after 2 years if Richard borrowed a sum of $3300 at a 5% simple interest?

(8) Richard took a loan of $5200 at the rate of 8% simple interest per annum. If he paid an amount of $7696 to clear the loan, then find the time period of the loan.

(9) What amount does John have to pay after 5 years if he takes a loan of $3200 at 4% simple interest?

(10) If Ashley paid $5278 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.