Simple Interest
Math MCQs

Question :    How much loan did Paul borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8040 to clear it?

Correct Answer  $6700

Solution & Explanation

Solution

Given,

Amount (A) = $8040

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

$8040 = P (1 + 4% × 5)

⇒ $8040 = P (1 + ⁴/₁₀₀ × 5)

⇒ $8040 = P (1 + ^{4 × 5}/₁₀₀)

⇒ $8040 = P (1 + ²⁰/₁₀₀)

⇒ $8040 = P (^{100 + 20}/₁₀₀)

⇒ $8040 = P × ¹²⁰/₁₀₀

⇒ P × ¹²⁰/₁₀₀ = $8040

⇒ P = ⁸⁰⁴⁰/_¹²⁰/100

⇒ P = 8040 × ¹⁰⁰/₁₂₀

⇒ P = ^{8040 × 100}/₁₂₀

⇒ P = ⁸⁰⁴⁰⁰⁰/₁₂₀

⇒ P = $6700

Thus, the sum borrowed (P) = $6700 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 8040, then the Principal = ¹⁰⁰/₁₂₀ × 8040

= ^{100 × 8040}/₁₂₀

= ⁸⁰⁴⁰⁰⁰/₁₂₀

= 6700

Thus, Principal = $6700

Thus, the sum borrowed = $6700 Answer

Similar Questions

(1) Linda took a loan of $4700 at the rate of 7% simple interest per annum. If he paid an amount of $7661 to clear the loan, then find the time period of the loan.

(2) What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 10% simple interest?

(3) John took a loan of $4400 at the rate of 7% simple interest per annum. If he paid an amount of $7172 to clear the loan, then find the time period of the loan.

(4) Charles took a loan of $5800 at the rate of 10% simple interest per annum. If he paid an amount of $9860 to clear the loan, then find the time period of the loan.

(5) Nancy took a loan of $6300 at the rate of 7% simple interest per annum. If he paid an amount of $10269 to clear the loan, then find the time period of the loan.

(6) What amount will be due after 2 years if William borrowed a sum of $3250 at a 7% simple interest?

(7) If David paid $4080 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(8) Calculate the amount due after 10 years if Charles borrowed a sum of $5900 at a rate of 3% simple interest.

(9) Find the amount to be paid if Christopher borrowed a sum of $6000 at 3% simple interest for 7 years.

(10) Find the amount to be paid if Patricia borrowed a sum of $5150 at 7% simple interest for 8 years.