Simple Interest
Math MCQs

Question :    If Linda paid $3886 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

Correct Answer  $3350

Solution & Explanation

Solution

Given,

Amount (A) = $3886

Rate of Simple Interest (R) = 4%

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

$3886 = P (1 + 4% × 4)

⇒ $3886 = P (1 + ⁴/₁₀₀ × 4)

⇒ $3886 = P (1 + ^{4 × 4}/₁₀₀)

⇒ $3886 = P (1 + ¹⁶/₁₀₀)

⇒ $3886 = P (^{100 + 16}/₁₀₀)

⇒ $3886 = P × ¹¹⁶/₁₀₀

⇒ P × ¹¹⁶/₁₀₀ = $3886

⇒ P = ³⁸⁸⁶/_¹¹⁶/100

⇒ P = 3886 × ¹⁰⁰/₁₁₆

⇒ P = ^{3886 × 100}/₁₁₆

⇒ P = ³⁸⁸⁶⁰⁰/₁₁₆

⇒ P = $3350

Thus, the sum borrowed (P) = $3350 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 = 4% per annum

Thus, Interest = 4% of principal

⇒ Interest = 4% of 100 = 4

Thus, Simple Interest for 1 year = 4

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 × 4 = 16

Thus, simple interest for 4 years = 16

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 16 = 116

Calculation of the Principal

Now,

∵ If the Amount is 116, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₁₆

∴ If the Amount is 3886, then the Principal = ¹⁰⁰/₁₁₆ × 3886

= ^{100 × 3886}/₁₁₆

= ³⁸⁸⁶⁰⁰/₁₁₆

= 3350

Thus, Principal = $3350

Thus, the sum borrowed = $3350 Answer

Similar Questions

(1) What amount does Michael have to pay after 5 years if he takes a loan of $3300 at 8% simple interest?

(2) What amount will be due after 2 years if Christopher borrowed a sum of $3500 at a 5% simple interest?

(3) Calculate the amount due after 9 years if Jennifer borrowed a sum of $5250 at a rate of 7% simple interest.

(4) Patricia took a loan of $4300 at the rate of 8% simple interest per annum. If he paid an amount of $7740 to clear the loan, then find the time period of the loan.

(5) Barbara took a loan of $5100 at the rate of 8% simple interest per annum. If he paid an amount of $7956 to clear the loan, then find the time period of the loan.

(6) Calculate the amount due if David borrowed a sum of $3400 at 8% simple interest for 4 years.

(7) Donald took a loan of $7000 at the rate of 8% simple interest per annum. If he paid an amount of $11480 to clear the loan, then find the time period of the loan.

(8) Calculate the amount due if Christopher borrowed a sum of $4000 at 7% simple interest for 3 years.

(9) Margaret took a loan of $6700 at the rate of 9% simple interest per annum. If he paid an amount of $10318 to clear the loan, then find the time period of the loan.

(10) William took a loan of $5000 at the rate of 6% simple interest per annum. If he paid an amount of $6800 to clear the loan, then find the time period of the loan.