Simple Interest
Math MCQs

Question :    If James paid $3600 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

Correct Answer  $3000

Solution & Explanation

Solution

Given,

Amount (A) = $3600

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

$3600 = P (1 + 5% × 4)

⇒ $3600 = P (1 + ⁵/₁₀₀ × 4)

⇒ $3600 = P (1 + ^{5 × 4}/₁₀₀)

⇒ $3600 = P (1 + ²⁰/₁₀₀)

⇒ $3600 = P (^{100 + 20}/₁₀₀)

⇒ $3600 = P × ¹²⁰/₁₀₀

⇒ P × ¹²⁰/₁₀₀ = $3600

⇒ P = ³⁶⁰⁰/_¹²⁰/100

⇒ P = 3600 × ¹⁰⁰/₁₂₀

⇒ P = ^{3600 × 100}/₁₂₀

⇒ P = ³⁶⁰⁰⁰⁰/₁₂₀

⇒ P = $3000

Thus, the sum borrowed (P) = $3000 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 3600, then the Principal = ¹⁰⁰/₁₂₀ × 3600

= ^{100 × 3600}/₁₂₀

= ³⁶⁰⁰⁰⁰/₁₂₀

= 3000

Thus, Principal = $3000

Thus, the sum borrowed = $3000 Answer

Similar Questions

(1) 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.

(2) Calculate the amount due after 9 years if Elizabeth borrowed a sum of $5450 at a rate of 4% simple interest.

(3) Nancy took a loan of $6300 at the rate of 10% simple interest per annum. If he paid an amount of $10710 to clear the loan, then find the time period of the loan.

(4) In how much time a principal of $3100 will amount to $3410 at a simple interest of 5% per annum?

(5) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 9% simple interest for 8 years.

(6) Find the amount to be paid if Linda borrowed a sum of $5350 at 3% simple interest for 8 years.

(7) Elizabeth took a loan of $4900 at the rate of 6% simple interest per annum. If he paid an amount of $6958 to clear the loan, then find the time period of the loan.

(8) What amount will be due after 2 years if James borrowed a sum of $3000 at a 6% simple interest?

(9) Find the amount to be paid if Mary borrowed a sum of $5050 at 8% simple interest for 7 years.

(10) How much loan did Timothy borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8140 to clear it?