Simple Interest
Math MCQs

Question :    If Barbara paid $3976 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

Correct Answer  $3550

Solution & Explanation

Solution

Given,

Amount (A) = $3976

Rate of Simple Interest (R) = 3%

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

$3976 = P (1 + 3% × 4)

⇒ $3976 = P (1 + ³/₁₀₀ × 4)

⇒ $3976 = P (1 + ^{3 × 4}/₁₀₀)

⇒ $3976 = P (1 + ¹²/₁₀₀)

⇒ $3976 = P (^{100 + 12}/₁₀₀)

⇒ $3976 = P × ¹¹²/₁₀₀

⇒ P × ¹¹²/₁₀₀ = $3976

⇒ P = ³⁹⁷⁶/_¹¹²/100

⇒ P = 3976 × ¹⁰⁰/₁₁₂

⇒ P = ^{3976 × 100}/₁₁₂

⇒ P = ³⁹⁷⁶⁰⁰/₁₁₂

⇒ P = $3550

Thus, the sum borrowed (P) = $3550 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 = 3% per annum

Thus, Interest = 3% of principal

⇒ Interest = 3% of 100 = 3

Thus, Simple Interest for 1 year = 3

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 × 3 = 12

Thus, simple interest for 4 years = 12

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 12 = 112

Calculation of the Principal

Now,

∵ If the Amount is 112, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₁₂

∴ If the Amount is 3976, then the Principal = ¹⁰⁰/₁₁₂ × 3976

= ^{100 × 3976}/₁₁₂

= ³⁹⁷⁶⁰⁰/₁₁₂

= 3550

Thus, Principal = $3550

Thus, the sum borrowed = $3550 Answer

Similar Questions

(1) Andrew had to pay $5088 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(2) If Michelle paid $5742 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(3) Calculate the amount due if Joseph borrowed a sum of $3700 at 10% simple interest for 4 years.

(4) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 4% simple interest?

(5) Find the amount to be paid if Susan borrowed a sum of $5650 at 10% simple interest for 8 years.

(6) How much loan did Dorothy borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8337.5 to clear it?

(7) In how much time a principal of $3100 will amount to $3875 at a simple interest of 5% per annum?

(8) Find the amount to be paid if Christopher borrowed a sum of $6000 at 7% simple interest for 7 years.

(9) Mark took a loan of $6800 at the rate of 9% simple interest per annum. If he paid an amount of $11084 to clear the loan, then find the time period of the loan.

(10) Susan took a loan of $5300 at the rate of 9% simple interest per annum. If he paid an amount of $9593 to clear the loan, then find the time period of the loan.