Simple Interest
Math MCQs

Question :    If Patricia paid $3402 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

Correct Answer  $3150

Solution & Explanation

Solution

Given,

Amount (A) = $3402

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

$3402 = P (1 + 2% × 4)

⇒ $3402 = P (1 + ²/₁₀₀ × 4)

⇒ $3402 = P (1 + ^{2 × 4}/₁₀₀)

⇒ $3402 = P (1 + ⁸/₁₀₀)

⇒ $3402 = P (^{100 + 8}/₁₀₀)

⇒ $3402 = P × ¹⁰⁸/₁₀₀

⇒ P × ¹⁰⁸/₁₀₀ = $3402

⇒ P = ³⁴⁰²/_¹⁰⁸/100

⇒ P = 3402 × ¹⁰⁰/₁₀₈

⇒ P = ^{3402 × 100}/₁₀₈

⇒ P = ³⁴⁰²⁰⁰/₁₀₈

⇒ P = $3150

Thus, the sum borrowed (P) = $3150 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 3402, then the Principal = ¹⁰⁰/₁₀₈ × 3402

= ^{100 × 3402}/₁₀₈

= ³⁴⁰²⁰⁰/₁₀₈

= 3150

Thus, Principal = $3150

Thus, the sum borrowed = $3150 Answer

Similar Questions

(1) If John borrowed $3200 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.

(2) Elizabeth took a loan of $4900 at the rate of 7% simple interest per annum. If he paid an amount of $7644 to clear the loan, then find the time period of the loan.

(3) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 5% simple interest for 4 years.

(4) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 8% simple interest?

(5) How much loan did Cynthia borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9540 to clear it?

(6) What amount does Thomas have to pay after 6 years if he takes a loan of $3800 at 4% simple interest?

(7) In how much time a principal of $3050 will amount to $3355 at a simple interest of 5% per annum?

(8) Charles took a loan of $5800 at the rate of 10% simple interest per annum. If he paid an amount of $9860 to clear the loan, then find the time period of the loan.

(9) Find the amount to be paid if John borrowed a sum of $5200 at 9% simple interest for 7 years.

(10) Karen had to pay $4187 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.