Simple Interest
Math MCQs

Question :  ( 1 of 10 )  If Mary paid $3538 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

Correct Answer  $3050

Solution & Explanation

Solution

Given,

Amount (A) = $3538

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

$3538 = P (1 + 4% × 4)

⇒ $3538 = P (1 + ⁴/₁₀₀ × 4)

⇒ $3538 = P (1 + ^{4 × 4}/₁₀₀)

⇒ $3538 = P (1 + ¹⁶/₁₀₀)

⇒ $3538 = P (^{100 + 16}/₁₀₀)

⇒ $3538 = P × ¹¹⁶/₁₀₀

⇒ P × ¹¹⁶/₁₀₀ = $3538

⇒ P = ³⁵³⁸/_¹¹⁶/100

⇒ P = 3538 × ¹⁰⁰/₁₁₆

⇒ P = ^{3538 × 100}/₁₁₆

⇒ P = ³⁵³⁸⁰⁰/₁₁₆

⇒ P = $3050

Thus, the sum borrowed (P) = $3050 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 3538, then the Principal = ¹⁰⁰/₁₁₆ × 3538

= ^{100 × 3538}/₁₁₆

= ³⁵³⁸⁰⁰/₁₁₆

= 3050

Thus, Principal = $3050

Thus, the sum borrowed = $3050 Answer

Similar Questions

(1) William took a loan of $5000 at the rate of 8% 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 Jennifer have to pay after 6 years if he takes a loan of $3250 at 4% simple interest?

(3) Sarah took a loan of $5700 at the rate of 7% simple interest per annum. If he paid an amount of $8892 to clear the loan, then find the time period of the loan.

(4) Calculate the amount due if John borrowed a sum of $3200 at 8% simple interest for 3 years.

(5) Calculate the amount due if Jennifer borrowed a sum of $3250 at 7% simple interest for 4 years.

(6) Find the amount to be paid if Joseph borrowed a sum of $5700 at 5% simple interest for 7 years.

(7) Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 5% simple interest.

(8) Calculate the amount due after 10 years if Barbara borrowed a sum of $5550 at a rate of 10% simple interest.

(9) Find the amount to be paid if John borrowed a sum of $5200 at 5% simple interest for 8 years.

(10) If Barbara paid $4118 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.