Simple Interest
Math MCQs

Question :    How much loan did David borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6480 to clear it?

Correct Answer  $5400

Solution & Explanation

Solution

Given,

Amount (A) = $6480

Rate of Simple Interest (R) = 4%

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

$6480 = P (1 + 4% × 5)

⇒ $6480 = P (1 + ⁴/₁₀₀ × 5)

⇒ $6480 = P (1 + ^{4 × 5}/₁₀₀)

⇒ $6480 = P (1 + ²⁰/₁₀₀)

⇒ $6480 = P (^{100 + 20}/₁₀₀)

⇒ $6480 = P × ¹²⁰/₁₀₀

⇒ P × ¹²⁰/₁₀₀ = $6480

⇒ P = ⁶⁴⁸⁰/_¹²⁰/100

⇒ P = 6480 × ¹⁰⁰/₁₂₀

⇒ P = ^{6480 × 100}/₁₂₀

⇒ P = ⁶⁴⁸⁰⁰⁰/₁₂₀

⇒ 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 = 4% per annum

Thus, Interest = 4% of principal

⇒ Interest = 4% of 100 = 4

Thus, Simple Interest for 1 year = 4

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 × 4 = 20

Thus, simple interest for 5 years = 20

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 20 = 120

Calculation of the Principal

Now,

∵ If the Amount is 120, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₂₀

∴ If the Amount is 6480, then the Principal = ¹⁰⁰/₁₂₀ × 6480

= ^{100 × 6480}/₁₂₀

= ⁶⁴⁸⁰⁰⁰/₁₂₀

= 5400

Thus, Principal = $5400

Thus, the sum borrowed = $5400 Answer

Similar Questions

(1) Thomas had to pay $4370 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(2) Find the amount to be paid if Mary borrowed a sum of $5050 at 10% simple interest for 7 years.

(3) Calculate the amount due if Karen borrowed a sum of $3950 at 9% simple interest for 4 years.

(4) Robert took a loan of $4200 at the rate of 10% simple interest per annum. If he paid an amount of $8400 to clear the loan, then find the time period of the loan.

(5) Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 3% simple interest.

(6) Barbara took a loan of $5100 at the rate of 7% simple interest per annum. If he paid an amount of $8313 to clear the loan, then find the time period of the loan.

(7) How much loan did Thomas borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6960 to clear it?

(8) Donald took a loan of $7000 at the rate of 6% simple interest per annum. If he paid an amount of $11200 to clear the loan, then find the time period of the loan.

(9) Calculate the amount due if Linda borrowed a sum of $3350 at 4% simple interest for 4 years.

(10) What amount will be due after 2 years if Donald borrowed a sum of $3750 at a 7% simple interest?