Simple Interest
Math MCQs

Question :    If Kenneth paid $5400 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

Correct Answer  $5000

Solution & Explanation

Solution

Given,

Amount (A) = $5400

Rate of Simple Interest (R) = 2%

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 + 2% × 4)

⇒ $5400 = P (1 + ²/₁₀₀ × 4)

⇒ $5400 = P (1 + ^{2 × 4}/₁₀₀)

⇒ $5400 = P (1 + ⁸/₁₀₀)

⇒ $5400 = P (^{100 + 8}/₁₀₀)

⇒ $5400 = P × ¹⁰⁸/₁₀₀

⇒ P × ¹⁰⁸/₁₀₀ = $5400

⇒ P = ⁵⁴⁰⁰/_¹⁰⁸/100

⇒ P = 5400 × ¹⁰⁰/₁₀₈

⇒ P = ^{5400 × 100}/₁₀₈

⇒ P = ⁵⁴⁰⁰⁰⁰/₁₀₈

⇒ P = $5000

Thus, the sum borrowed (P) = $5000 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 = 2% per annum

Thus, Interest = 2% of principal

⇒ Interest = 2% of 100 = 2

Thus, Simple Interest for 1 year = 2

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 × 2 = 8

Thus, simple interest for 4 years = 8

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 8 = 108

Calculation of the Principal

Now,

∵ If the Amount is 108, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₀₈

∴ If the Amount is 5400, then the Principal = ¹⁰⁰/₁₀₈ × 5400

= ^{100 × 5400}/₁₀₈

= ⁵⁴⁰⁰⁰⁰/₁₀₈

= 5000

Thus, Principal = $5000

Thus, the sum borrowed = $5000 Answer

Similar Questions

(1) What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 8% simple interest?

(2) What amount does Jennifer have to pay after 6 years if he takes a loan of $3250 at 4% simple interest?

(3) William took a loan of $5000 at the rate of 9% simple interest per annum. If he paid an amount of $8150 to clear the loan, then find the time period of the loan.

(4) Calculate the amount due after 10 years if Mary borrowed a sum of $5050 at a rate of 6% simple interest.

(5) Find the amount to be paid if Thomas borrowed a sum of $5800 at 6% simple interest for 7 years.

(6) What amount will be due after 2 years if Robert borrowed a sum of $3050 at a 7% simple interest?

(7) David took a loan of $4800 at the rate of 9% simple interest per annum. If he paid an amount of $7824 to clear the loan, then find the time period of the loan.

(8) Calculate the amount due after 10 years if Richard borrowed a sum of $5600 at a rate of 6% simple interest.

(9) How much loan did James borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6250 to clear it?

(10) What amount does Barbara have to pay after 5 years if he takes a loan of $3550 at 4% simple interest?