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) How much loan did Christopher borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7200 to clear it?

(2) Sandra took a loan of $6900 at the rate of 9% simple interest per annum. If he paid an amount of $11868 to clear the loan, then find the time period of the loan.

(3) Find the amount to be paid if Robert borrowed a sum of $5100 at 9% simple interest for 7 years.

(4) What amount does Elizabeth have to pay after 6 years if he takes a loan of $3450 at 3% simple interest?

(5) How much loan did Andrew borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8500 to clear it?

(6) What amount will be due after 2 years if Mark borrowed a sum of $3700 at a 9% simple interest?

(7) Calculate the amount due after 9 years if Elizabeth borrowed a sum of $5450 at a rate of 8% simple interest.

(8) How much loan did Emily borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7425 to clear it?

(9) Calculate the amount due after 9 years if Sarah borrowed a sum of $5850 at a rate of 8% simple interest.

(10) Calculate the amount due after 10 years if Jennifer borrowed a sum of $5250 at a rate of 6% simple interest.