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) Patricia took a loan of $4300 at the rate of 10% simple interest per annum. If he paid an amount of $8600 to clear the loan, then find the time period of the loan.

(2) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 6% simple interest?

(3) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 8% simple interest for 7 years.

(4) Matthew had to pay $4452 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(5) Find the amount to be paid if William borrowed a sum of $5500 at 3% simple interest for 7 years.

(6) How much loan did Richard borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7000 to clear it?

(7) How much loan did Deborah borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8567.5 to clear it?

(8) Calculate the amount due after 10 years if Karen borrowed a sum of $5950 at a rate of 10% simple interest.

(9) Patricia had to pay $3528 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(10) Margaret took a loan of $6700 at the rate of 6% simple interest per annum. If he paid an amount of $10720 to clear the loan, then find the time period of the loan.