Simple Interest
Math MCQs

Question :    If David paid $3944 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

Correct Answer  $3400

Solution & Explanation

Solution

Given,

Amount (A) = $3944

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

$3944 = P (1 + 4% × 4)

⇒ $3944 = P (1 + ⁴/₁₀₀ × 4)

⇒ $3944 = P (1 + ^{4 × 4}/₁₀₀)

⇒ $3944 = P (1 + ¹⁶/₁₀₀)

⇒ $3944 = P (^{100 + 16}/₁₀₀)

⇒ $3944 = P × ¹¹⁶/₁₀₀

⇒ P × ¹¹⁶/₁₀₀ = $3944

⇒ P = ³⁹⁴⁴/_¹¹⁶/100

⇒ P = 3944 × ¹⁰⁰/₁₁₆

⇒ P = ^{3944 × 100}/₁₁₆

⇒ P = ³⁹⁴⁴⁰⁰/₁₁₆

⇒ P = $3400

Thus, the sum borrowed (P) = $3400 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 3944, then the Principal = ¹⁰⁰/₁₁₆ × 3944

= ^{100 × 3944}/₁₁₆

= ³⁹⁴⁴⁰⁰/₁₁₆

= 3400

Thus, Principal = $3400

Thus, the sum borrowed = $3400 Answer

Similar Questions

(1) Calculate the amount due after 10 years if John borrowed a sum of $5200 at a rate of 7% simple interest.

(2) Calculate the amount due after 10 years if Sarah borrowed a sum of $5850 at a rate of 4% simple interest.

(3) Barbara had to pay $3976 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(4) Mary had to pay $3507.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(5) How much loan did Sandra borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7417.5 to clear it?

(6) What amount does William have to pay after 6 years if he takes a loan of $3500 at 4% simple interest?

(7) What amount will be due after 2 years if Charles borrowed a sum of $3450 at a 9% simple interest?

(8) Margaret had to pay $4872 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(9) What amount does Linda have to pay after 5 years if he takes a loan of $3350 at 3% simple interest?

(10) Susan took a loan of $5300 at the rate of 6% simple interest per annum. If he paid an amount of $7844 to clear the loan, then find the time period of the loan.