Simple Interest
Math MCQs

Question :  ( 1 of 10 )  How much loan did Robert borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $5865 to clear it?

Correct Answer  $5100

Solution & Explanation

Solution

Given,

Amount (A) = $5865

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

$5865 = P (1 + 3% × 5)

⇒ $5865 = P (1 + ³/₁₀₀ × 5)

⇒ $5865 = P (1 + ^{3 × 5}/₁₀₀)

⇒ $5865 = P (1 + ¹⁵/₁₀₀)

⇒ $5865 = P (^{100 + 15}/₁₀₀)

⇒ $5865 = P × ¹¹⁵/₁₀₀

⇒ P × ¹¹⁵/₁₀₀ = $5865

⇒ P = ⁵⁸⁶⁵/_¹¹⁵/100

⇒ P = 5865 × ¹⁰⁰/₁₁₅

⇒ P = ^{5865 × 100}/₁₁₅

⇒ P = ⁵⁸⁶⁵⁰⁰/₁₁₅

⇒ P = $5100

Thus, the sum borrowed (P) = $5100 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 5865, then the Principal = ¹⁰⁰/₁₁₅ × 5865

= ^{100 × 5865}/₁₁₅

= ⁵⁸⁶⁵⁰⁰/₁₁₅

= 5100

Thus, Principal = $5100

Thus, the sum borrowed = $5100 Answer

Similar Questions

(1) Calculate the amount due if Richard borrowed a sum of $3600 at 9% simple interest for 4 years.

(2) Calculate the amount due if James borrowed a sum of $3000 at 10% simple interest for 4 years.

(3) How much loan did Timothy borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8140 to clear it?

(4) Michael had to pay $3795 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(5) Calculate the amount due after 9 years if Joseph borrowed a sum of $5700 at a rate of 3% simple interest.

(6) Daniel had to pay $4592 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(7) Elizabeth took a loan of $4900 at the rate of 8% simple interest per annum. If he paid an amount of $8820 to clear the loan, then find the time period of the loan.

(8) Joseph took a loan of $5400 at the rate of 9% simple interest per annum. If he paid an amount of $8802 to clear the loan, then find the time period of the loan.

(9) What amount does William have to pay after 5 years if he takes a loan of $3500 at 9% simple interest?

(10) How much loan did Robert borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6120 to clear it?