Simple Interest
Math MCQs

Question :  ( 1 of 10 )  How much loan did Charles borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6785 to clear it?

Correct Answer  $5900

Solution & Explanation

Solution

Given,

Amount (A) = $6785

Rate of Simple Interest (R) = 3%

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

$6785 = P (1 + 3% × 5)

⇒ $6785 = P (1 + ³/₁₀₀ × 5)

⇒ $6785 = P (1 + ^{3 × 5}/₁₀₀)

⇒ $6785 = P (1 + ¹⁵/₁₀₀)

⇒ $6785 = P (^{100 + 15}/₁₀₀)

⇒ $6785 = P × ¹¹⁵/₁₀₀

⇒ P × ¹¹⁵/₁₀₀ = $6785

⇒ P = ⁶⁷⁸⁵/_¹¹⁵/100

⇒ P = 6785 × ¹⁰⁰/₁₁₅

⇒ P = ^{6785 × 100}/₁₁₅

⇒ P = ⁶⁷⁸⁵⁰⁰/₁₁₅

⇒ P = $5900

Thus, the sum borrowed (P) = $5900 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 = 3% per annum

Thus, Interest = 3% of principal

⇒ Interest = 3% of 100 = 3

Thus, Simple Interest for 1 year = 3

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 × 3 = 15

Thus, simple interest for 5 years = 15

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 15 = 115

Calculation of the Principal

Now,

∵ If the Amount is 115, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₁₅

∴ If the Amount is 6785, then the Principal = ¹⁰⁰/₁₁₅ × 6785

= ^{100 × 6785}/₁₁₅

= ⁶⁷⁸⁵⁰⁰/₁₁₅

= 5900

Thus, Principal = $5900

Thus, the sum borrowed = $5900 Answer

Similar Questions

(1) Calculate the amount due after 10 years if Mary borrowed a sum of $5050 at a rate of 5% simple interest.

(2) What amount does Jessica have to pay after 6 years if he takes a loan of $3750 at 8% simple interest?

(3) What amount will be due after 2 years if Andrew borrowed a sum of $3900 at a 9% simple interest?

(4) How much loan did William borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6600 to clear it?

(5) Thomas took a loan of $5600 at the rate of 7% simple interest per annum. If he paid an amount of $7952 to clear the loan, then find the time period of the loan.

(6) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 10% simple interest.

(7) Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 7% simple interest.

(8) Anthony took a loan of $6600 at the rate of 10% simple interest per annum. If he paid an amount of $12540 to clear the loan, then find the time period of the loan.

(9) Calculate the amount due if Jennifer borrowed a sum of $3250 at 7% simple interest for 3 years.

(10) If Donna paid $5238 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.