Simple Interest
Math MCQs

Question :    Lisa had to pay $4657.5 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  $4050

Solution & Explanation

Solution

Given,

Amount (A) = $4657.5

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

$4657.5 = P (1 + 5% × 3)

⇒ $4657.5 = P (1 + ⁵/₁₀₀ × 3)

⇒ $4657.5 = P (1 + ^{5 × 3}/₁₀₀)

⇒ $4657.5 = P (1 + ¹⁵/₁₀₀)

⇒ $4657.5 = P (^{100 + 15}/₁₀₀)

⇒ $4657.5 = P × ¹¹⁵/₁₀₀

⇒ P × ¹¹⁵/₁₀₀ = $4657.5

⇒ P = ^4657.5/_¹¹⁵/100

⇒ P = 4657.5 × ¹⁰⁰/₁₁₅

⇒ P = ^{4657.5 × 100}/₁₁₅

⇒ P = ⁴⁶⁵⁷⁵⁰/₁₁₅

⇒ P = $4050

Thus, the sum borrowed (P) = $4050 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 4657.5, then the Principal = ¹⁰⁰/₁₁₅ × 4657.5

= ^{100 × 4657.5}/₁₁₅

= ⁴⁶⁵⁷⁵⁰/₁₁₅

= 4050

Thus, Principal = $4050

Thus, the sum borrowed = $4050 Answer

Similar Questions

(1) Calculate the amount due after 9 years if Linda borrowed a sum of $5350 at a rate of 3% simple interest.

(2) How much loan did Brian borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8280 to clear it?

(3) Find the amount to be paid if Christopher borrowed a sum of $6000 at 8% simple interest for 7 years.

(4) What amount will be due after 2 years if Anthony borrowed a sum of $3650 at a 4% simple interest?

(5) Calculate the amount due if William borrowed a sum of $3500 at 10% simple interest for 3 years.

(6) Find the amount to be paid if Robert borrowed a sum of $5100 at 9% simple interest for 7 years.

(7) If Karen borrowed $3950 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.

(8) Calculate the amount due after 10 years if Thomas borrowed a sum of $5800 at a rate of 2% simple interest.

(9) If William paid $4060 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(10) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 9% simple interest for 8 years.