Simple Interest
Math MCQs

Question :    Donald had to pay $5175 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  $4500

Solution & Explanation

Solution

Given,

Amount (A) = $5175

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

$5175 = P (1 + 5% × 3)

⇒ $5175 = P (1 + ⁵/₁₀₀ × 3)

⇒ $5175 = P (1 + ^{5 × 3}/₁₀₀)

⇒ $5175 = P (1 + ¹⁵/₁₀₀)

⇒ $5175 = P (^{100 + 15}/₁₀₀)

⇒ $5175 = P × ¹¹⁵/₁₀₀

⇒ P × ¹¹⁵/₁₀₀ = $5175

⇒ P = ⁵¹⁷⁵/_¹¹⁵/100

⇒ P = 5175 × ¹⁰⁰/₁₁₅

⇒ P = ^{5175 × 100}/₁₁₅

⇒ P = ⁵¹⁷⁵⁰⁰/₁₁₅

⇒ P = $4500

Thus, the sum borrowed (P) = $4500 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 5175, then the Principal = ¹⁰⁰/₁₁₅ × 5175

= ^{100 × 5175}/₁₁₅

= ⁵¹⁷⁵⁰⁰/₁₁₅

= 4500

Thus, Principal = $4500

Thus, the sum borrowed = $4500 Answer

Similar Questions

(1) Linda took a loan of $4700 at the rate of 6% simple interest per annum. If he paid an amount of $6392 to clear the loan, then find the time period of the loan.

(2) Susan took a loan of $5300 at the rate of 7% simple interest per annum. If he paid an amount of $8639 to clear the loan, then find the time period of the loan.

(3) Christopher took a loan of $6000 at the rate of 7% simple interest per annum. If he paid an amount of $10200 to clear the loan, then find the time period of the loan.

(4) What amount does David have to pay after 5 years if he takes a loan of $3400 at 4% simple interest?

(5) Find the amount to be paid if John borrowed a sum of $5200 at 2% simple interest for 8 years.

(6) Jennifer took a loan of $4500 at the rate of 6% simple interest per annum. If he paid an amount of $6660 to clear the loan, then find the time period of the loan.

(7) In how much time a principal of $3150 will amount to $3339 at a simple interest of 3% per annum?

(8) Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 6% simple interest.

(9) Michael took a loan of $4600 at the rate of 7% simple interest per annum. If he paid an amount of $7498 to clear the loan, then find the time period of the loan.

(10) Lisa took a loan of $6100 at the rate of 10% simple interest per annum. If he paid an amount of $9760 to clear the loan, then find the time period of the loan.