Simple Interest
Math MCQs

Question :    Kenneth had to pay $5750 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  $5000

Solution & Explanation

Solution

Given,

Amount (A) = $5750

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

$5750 = P (1 + 5% × 3)

⇒ $5750 = P (1 + ⁵/₁₀₀ × 3)

⇒ $5750 = P (1 + ^{5 × 3}/₁₀₀)

⇒ $5750 = P (1 + ¹⁵/₁₀₀)

⇒ $5750 = P (^{100 + 15}/₁₀₀)

⇒ $5750 = P × ¹¹⁵/₁₀₀

⇒ P × ¹¹⁵/₁₀₀ = $5750

⇒ P = ⁵⁷⁵⁰/_¹¹⁵/100

⇒ P = 5750 × ¹⁰⁰/₁₁₅

⇒ P = ^{5750 × 100}/₁₁₅

⇒ P = ⁵⁷⁵⁰⁰⁰/₁₁₅

⇒ P = $5000

Thus, the sum borrowed (P) = $5000 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 5750, then the Principal = ¹⁰⁰/₁₁₅ × 5750

= ^{100 × 5750}/₁₁₅

= ⁵⁷⁵⁰⁰⁰/₁₁₅

= 5000

Thus, Principal = $5000

Thus, the sum borrowed = $5000 Answer

Similar Questions

(1) What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 4% simple interest?

(2) Christopher took a loan of $6000 at the rate of 9% simple interest per annum. If he paid an amount of $9240 to clear the loan, then find the time period of the loan.

(3) What amount will be due after 2 years if Christopher borrowed a sum of $3500 at a 7% simple interest?

(4) Margaret took a loan of $6700 at the rate of 10% simple interest per annum. If he paid an amount of $12730 to clear the loan, then find the time period of the loan.

(5) Calculate the amount due if Robert borrowed a sum of $3100 at 9% simple interest for 4 years.

(6) Sandra had to pay $4850.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(7) In how much time a principal of $3000 will amount to $3180 at a simple interest of 3% per annum?

(8) Calculate the amount due after 10 years if Jessica borrowed a sum of $5750 at a rate of 8% simple interest.

(9) Anthony took a loan of $6600 at the rate of 6% simple interest per annum. If he paid an amount of $8976 to clear the loan, then find the time period of the loan.

(10) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 4% simple interest?