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) David took a loan of $4800 at the rate of 9% simple interest per annum. If he paid an amount of $8256 to clear the loan, then find the time period of the loan.

(2) If Donald paid $5400 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(3) Find the amount to be paid if Michael borrowed a sum of $5300 at 7% simple interest for 8 years.

(4) Find the amount to be paid if Patricia borrowed a sum of $5150 at 3% simple interest for 8 years.

(5) What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 2% simple interest?

(6) What amount does Jessica have to pay after 5 years if he takes a loan of $3750 at 6% simple interest?

(7) What amount does Richard have to pay after 6 years if he takes a loan of $3600 at 4% simple interest?

(8) What amount does Karen have to pay after 6 years if he takes a loan of $3950 at 9% simple interest?

(9) Calculate the amount due if John borrowed a sum of $3200 at 2% simple interest for 3 years.

(10) Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 8% simple interest.