Simple Interest
Math MCQs

Question :    If Susan paid $3942 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

Correct Answer  $3650

Solution & Explanation

Solution

Given,

Amount (A) = $3942

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

$3942 = P (1 + 2% × 4)

⇒ $3942 = P (1 + ²/₁₀₀ × 4)

⇒ $3942 = P (1 + ^{2 × 4}/₁₀₀)

⇒ $3942 = P (1 + ⁸/₁₀₀)

⇒ $3942 = P (^{100 + 8}/₁₀₀)

⇒ $3942 = P × ¹⁰⁸/₁₀₀

⇒ P × ¹⁰⁸/₁₀₀ = $3942

⇒ P = ³⁹⁴²/_¹⁰⁸/100

⇒ P = 3942 × ¹⁰⁰/₁₀₈

⇒ P = ^{3942 × 100}/₁₀₈

⇒ P = ³⁹⁴²⁰⁰/₁₀₈

⇒ P = $3650

Thus, the sum borrowed (P) = $3650 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 3942, then the Principal = ¹⁰⁰/₁₀₈ × 3942

= ^{100 × 3942}/₁₀₈

= ³⁹⁴²⁰⁰/₁₀₈

= 3650

Thus, Principal = $3650

Thus, the sum borrowed = $3650 Answer

Similar Questions

(1) Calculate the amount due if Charles borrowed a sum of $3900 at 6% simple interest for 4 years.

(2) Calculate the amount due after 10 years if Michael borrowed a sum of $5300 at a rate of 2% simple interest.

(3) Jessica took a loan of $5500 at the rate of 10% simple interest per annum. If he paid an amount of $11000 to clear the loan, then find the time period of the loan.

(4) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 10% simple interest for 8 years.

(5) Find the amount to be paid if Susan borrowed a sum of $5650 at 2% simple interest for 8 years.

(6) How much loan did Joseph borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7125 to clear it?

(7) Mark took a loan of $6800 at the rate of 6% simple interest per annum. If he paid an amount of $10472 to clear the loan, then find the time period of the loan.

(8) How much loan did James borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5500 to clear it?

(9) Find the amount to be paid if Joseph borrowed a sum of $5700 at 9% simple interest for 7 years.

(10) If Charles paid $4368 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.