Simple Interest
Math MCQs

Question :    Mark had to pay $5060 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

Correct Answer  $4400

Solution & Explanation

Solution

Given,

Amount (A) = $5060

Rate of Simple Interest (R) = 5%

Time (T) = 3 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

$5060 = P (1 + 5% × 3)

⇒ $5060 = P (1 + ⁵/₁₀₀ × 3)

⇒ $5060 = P (1 + ^{5 × 3}/₁₀₀)

⇒ $5060 = P (1 + ¹⁵/₁₀₀)

⇒ $5060 = P (^{100 + 15}/₁₀₀)

⇒ $5060 = P × ¹¹⁵/₁₀₀

⇒ P × ¹¹⁵/₁₀₀ = $5060

⇒ P = ⁵⁰⁶⁰/_¹¹⁵/100

⇒ P = 5060 × ¹⁰⁰/₁₁₅

⇒ P = ^{5060 × 100}/₁₁₅

⇒ P = ⁵⁰⁶⁰⁰⁰/₁₁₅

⇒ P = $4400

Thus, the sum borrowed (P) = $4400 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 = 5% per annum

Thus, Interest = 5% of principal

⇒ Interest = 5% of 100 = 5

Thus, Simple Interest for 1 year = 5

Calculation of the Amount

Since, in the question, time = 3 years

So, we need to calculate the simple interest for the given time period, which is 3 years

Thus, Simple Interest for 3 years = 3 × Simple Interest for 1 year

= 3 × 5 = 15

Thus, simple interest for 3 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 5060, then the Principal = ¹⁰⁰/₁₁₅ × 5060

= ^{100 × 5060}/₁₁₅

= ⁵⁰⁶⁰⁰⁰/₁₁₅

= 4400

Thus, Principal = $4400

Thus, the sum borrowed = $4400 Answer

Similar Questions

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

(2) James took a loan of $4000 at the rate of 7% simple interest per annum. If he paid an amount of $5960 to clear the loan, then find the time period of the loan.

(3) Calculate the amount due after 9 years if Barbara borrowed a sum of $5550 at a rate of 5% simple interest.

(4) What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 6% simple interest?

(5) If William borrowed $3500 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.

(6) In how much time a principal of $3150 will amount to $3780 at a simple interest of 5% per annum?

(7) If Susan borrowed $3650 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.

(8) How much loan did Deborah borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9312.5 to clear it?

(9) How much loan did John borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5720 to clear it?

(10) Calculate the amount due after 9 years if Barbara borrowed a sum of $5550 at a rate of 7% simple interest.