Simple Interest
Math MCQs

Question :    How much loan did Mark borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8000 to clear it?

Correct Answer  $6400

Solution & Explanation

Solution

Given,

Amount (A) = $8000

Rate of Simple Interest (R) = 5%

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

$8000 = P (1 + 5% × 5)

⇒ $8000 = P (1 + ⁵/₁₀₀ × 5)

⇒ $8000 = P (1 + ^{5 × 5}/₁₀₀)

⇒ $8000 = P (1 + ²⁵/₁₀₀)

⇒ $8000 = P (^{100 + 25}/₁₀₀)

⇒ $8000 = P × ¹²⁵/₁₀₀

⇒ P × ¹²⁵/₁₀₀ = $8000

⇒ P = ⁸⁰⁰⁰/_¹²⁵/100

⇒ P = 8000 × ¹⁰⁰/₁₂₅

⇒ P = ^{8000 × 100}/₁₂₅

⇒ P = ⁸⁰⁰⁰⁰⁰/₁₂₅

⇒ P = $6400

Thus, the sum borrowed (P) = $6400 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 = 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 × 5 = 25

Thus, simple interest for 5 years = 25

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 25 = 125

Calculation of the Principal

Now,

∵ If the Amount is 125, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₂₅

∴ If the Amount is 8000, then the Principal = ¹⁰⁰/₁₂₅ × 8000

= ^{100 × 8000}/₁₂₅

= ⁸⁰⁰⁰⁰⁰/₁₂₅

= 6400

Thus, Principal = $6400

Thus, the sum borrowed = $6400 Answer

Similar Questions

(1) In how much time a principal of $3000 will amount to $3600 at a simple interest of 4% per annum?

(2) Paul had to pay $5405 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(3) How much loan did Laura borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9420 to clear it?

(4) Find the amount to be paid if Susan borrowed a sum of $5650 at 10% simple interest for 8 years.

(5) If Richard paid $3888 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(6) What amount does Thomas have to pay after 5 years if he takes a loan of $3800 at 6% simple interest?

(7) If Nancy paid $4980 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(8) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 4% simple interest for 8 years.

(9) Jennifer took a loan of $4500 at the rate of 6% simple interest per annum. If he paid an amount of $6120 to clear the loan, then find the time period of the loan.

(10) Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 3% simple interest.