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) What amount will be due after 2 years if Matthew borrowed a sum of $3600 at a 10% simple interest?

(2) Find the amount to be paid if Joseph borrowed a sum of $5700 at 4% simple interest for 7 years.

(3) Find the amount to be paid if Linda borrowed a sum of $5350 at 2% simple interest for 8 years.

(4) Sandra took a loan of $6900 at the rate of 7% simple interest per annum. If he paid an amount of $10281 to clear the loan, then find the time period of the loan.

(5) Nancy took a loan of $6300 at the rate of 9% simple interest per annum. If he paid an amount of $10836 to clear the loan, then find the time period of the loan.

(6) Margaret took a loan of $6700 at the rate of 6% simple interest per annum. If he paid an amount of $9514 to clear the loan, then find the time period of the loan.

(7) What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 7% simple interest?

(8) Calculate the amount due after 10 years if Joseph borrowed a sum of $5700 at a rate of 2% simple interest.

(9) Patricia had to pay $3528 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(10) Betty took a loan of $6500 at the rate of 8% simple interest per annum. If he paid an amount of $11180 to clear the loan, then find the time period of the loan.