Simple Interest
Math MCQs

Question :    If Donald paid $5400 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

Correct Answer  $4500

Solution & Explanation

Solution

Given,

Amount (A) = $5400

Rate of Simple Interest (R) = 5%

Time (T) = 4 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

$5400 = P (1 + 5% × 4)

⇒ $5400 = P (1 + ⁵/₁₀₀ × 4)

⇒ $5400 = P (1 + ^{5 × 4}/₁₀₀)

⇒ $5400 = P (1 + ²⁰/₁₀₀)

⇒ $5400 = P (^{100 + 20}/₁₀₀)

⇒ $5400 = P × ¹²⁰/₁₀₀

⇒ P × ¹²⁰/₁₀₀ = $5400

⇒ P = ⁵⁴⁰⁰/_¹²⁰/100

⇒ P = 5400 × ¹⁰⁰/₁₂₀

⇒ P = ^{5400 × 100}/₁₂₀

⇒ P = ⁵⁴⁰⁰⁰⁰/₁₂₀

⇒ P = $4500

Thus, the sum borrowed (P) = $4500 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 = 4 years

So, we need to calculate the simple interest for the given time period, which is 4 years

Thus, Simple Interest for 4 years = 4 × Simple Interest for 1 year

= 4 × 5 = 20

Thus, simple interest for 4 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 5400, then the Principal = ¹⁰⁰/₁₂₀ × 5400

= ^{100 × 5400}/₁₂₀

= ⁵⁴⁰⁰⁰⁰/₁₂₀

= 4500

Thus, Principal = $4500

Thus, the sum borrowed = $4500 Answer

Similar Questions

(1) How much loan did Richard borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6160 to clear it?

(2) Find the amount to be paid if Richard borrowed a sum of $5600 at 10% simple interest for 8 years.

(3) Anthony had to pay $4558 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(4) What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 10% simple interest?

(5) Betty took a loan of $6500 at the rate of 7% simple interest per annum. If he paid an amount of $11050 to clear the loan, then find the time period of the loan.

(6) Christopher had to pay $4600 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(7) How much loan did Barbara borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6382.5 to clear it?

(8) Calculate the amount due if Thomas borrowed a sum of $3800 at 10% simple interest for 4 years.

(9) How much loan did Emily borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8437.5 to clear it?

(10) What amount does Thomas have to pay after 6 years if he takes a loan of $3800 at 8% simple interest?