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) What amount does Karen have to pay after 6 years if he takes a loan of $3950 at 4% simple interest?

(2) Calculate the amount due after 9 years if Susan borrowed a sum of $5650 at a rate of 6% simple interest.

(3) David took a loan of $4800 at the rate of 10% simple interest per annum. If he paid an amount of $8640 to clear the loan, then find the time period of the loan.

(4) In how much time a principal of $3150 will amount to $3402 at a simple interest of 4% per annum?

(5) If Paul paid $5264 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(6) What amount will be due after 2 years if Donald borrowed a sum of $3750 at a 4% simple interest?

(7) Christopher took a loan of $6000 at the rate of 10% simple interest per annum. If he paid an amount of $10800 to clear the loan, then find the time period of the loan.

(8) William took a loan of $5000 at the rate of 10% simple interest per annum. If he paid an amount of $8500 to clear the loan, then find the time period of the loan.

(9) What amount will be due after 2 years if Daniel borrowed a sum of $3550 at a 5% simple interest?

(10) Thomas had to pay $4142 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.