Simple Interest
Math MCQs

Question :    If Steven paid $5152 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

Correct Answer  $4600

Solution & Explanation

Solution

Given,

Amount (A) = $5152

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

$5152 = P (1 + 3% × 4)

⇒ $5152 = P (1 + ³/₁₀₀ × 4)

⇒ $5152 = P (1 + ^{3 × 4}/₁₀₀)

⇒ $5152 = P (1 + ¹²/₁₀₀)

⇒ $5152 = P (^{100 + 12}/₁₀₀)

⇒ $5152 = P × ¹¹²/₁₀₀

⇒ P × ¹¹²/₁₀₀ = $5152

⇒ P = ⁵¹⁵²/_¹¹²/100

⇒ P = 5152 × ¹⁰⁰/₁₁₂

⇒ P = ^{5152 × 100}/₁₁₂

⇒ P = ⁵¹⁵²⁰⁰/₁₁₂

⇒ P = $4600

Thus, the sum borrowed (P) = $4600 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 5152, then the Principal = ¹⁰⁰/₁₁₂ × 5152

= ^{100 × 5152}/₁₁₂

= ⁵¹⁵²⁰⁰/₁₁₂

= 4600

Thus, Principal = $4600

Thus, the sum borrowed = $4600 Answer

Similar Questions

(1) Calculate the amount due if Richard borrowed a sum of $3600 at 10% simple interest for 4 years.

(2) Linda had to pay $3551 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(3) Anthony took a loan of $6600 at the rate of 7% simple interest per annum. If he paid an amount of $9372 to clear the loan, then find the time period of the loan.

(4) Find the amount to be paid if James borrowed a sum of $5000 at 10% simple interest for 7 years.

(5) Find the amount to be paid if Mary borrowed a sum of $5050 at 5% simple interest for 8 years.

(6) Find the amount to be paid if Patricia borrowed a sum of $5150 at 9% simple interest for 7 years.

(7) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 3% simple interest?

(8) What amount will be due after 2 years if Michael borrowed a sum of $3150 at a 6% simple interest?

(9) How much loan did Donna borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8562.5 to clear it?

(10) If Michael borrowed $3300 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.