Simple Interest
Math MCQs

Question :    How much loan did David borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6750 to clear it?

Correct Answer  $5400

Solution & Explanation

Solution

Given,

Amount (A) = $6750

Rate of Simple Interest (R) = 5%

Time (T) = 5 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

$6750 = P (1 + 5% × 5)

⇒ $6750 = P (1 + ⁵/₁₀₀ × 5)

⇒ $6750 = P (1 + ^{5 × 5}/₁₀₀)

⇒ $6750 = P (1 + ²⁵/₁₀₀)

⇒ $6750 = P (^{100 + 25}/₁₀₀)

⇒ $6750 = P × ¹²⁵/₁₀₀

⇒ P × ¹²⁵/₁₀₀ = $6750

⇒ P = ⁶⁷⁵⁰/_¹²⁵/100

⇒ P = 6750 × ¹⁰⁰/₁₂₅

⇒ P = ^{6750 × 100}/₁₂₅

⇒ P = ⁶⁷⁵⁰⁰⁰/₁₂₅

⇒ P = $5400

Thus, the sum borrowed (P) = $5400 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 = 5 years

So, we need to calculate the simple interest for the given time period, which is 5 years

Thus, Simple Interest for 5 years = 5 × Simple Interest for 1 year

= 5 × 5 = 25

Thus, simple interest for 5 years = 25

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 25 = 125

Calculation of the Principal

Now,

∵ If the Amount is 125, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₂₅

∴ If the Amount is 6750, then the Principal = ¹⁰⁰/₁₂₅ × 6750

= ^{100 × 6750}/₁₂₅

= ⁶⁷⁵⁰⁰⁰/₁₂₅

= 5400

Thus, Principal = $5400

Thus, the sum borrowed = $5400 Answer

Similar Questions

(1) Linda had to pay $3551 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(2) Robert took a loan of $4200 at the rate of 7% simple interest per annum. If he paid an amount of $6258 to clear the loan, then find the time period of the loan.

(3) Robert took a loan of $4200 at the rate of 6% simple interest per annum. If he paid an amount of $5712 to clear the loan, then find the time period of the loan.

(4) What amount does Elizabeth have to pay after 6 years if he takes a loan of $3450 at 6% simple interest?

(5) Calculate the amount due after 9 years if Jessica borrowed a sum of $5750 at a rate of 5% simple interest.

(6) Calculate the amount due if Christopher borrowed a sum of $4000 at 2% simple interest for 3 years.

(7) Calculate the amount due if Jennifer borrowed a sum of $3250 at 3% simple interest for 3 years.

(8) Michael took a loan of $4600 at the rate of 10% simple interest per annum. If he paid an amount of $7820 to clear the loan, then find the time period of the loan.

(9) Anthony took a loan of $6600 at the rate of 10% simple interest per annum. If he paid an amount of $10560 to clear the loan, then find the time period of the loan.

(10) Richard took a loan of $5200 at the rate of 9% simple interest per annum. If he paid an amount of $8944 to clear the loan, then find the time period of the loan.