Simple Interest
Math MCQs

Question :    Ashley had to pay $5096 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

Correct Answer  $4550

Solution & Explanation

Solution

Given,

Amount (A) = $5096

Rate of Simple Interest (R) = 4%

Time (T) = 3 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

$5096 = P (1 + 4% × 3)

⇒ $5096 = P (1 + ⁴/₁₀₀ × 3)

⇒ $5096 = P (1 + ^{4 × 3}/₁₀₀)

⇒ $5096 = P (1 + ¹²/₁₀₀)

⇒ $5096 = P (^{100 + 12}/₁₀₀)

⇒ $5096 = P × ¹¹²/₁₀₀

⇒ P × ¹¹²/₁₀₀ = $5096

⇒ P = ⁵⁰⁹⁶/_¹¹²/100

⇒ P = 5096 × ¹⁰⁰/₁₁₂

⇒ P = ^{5096 × 100}/₁₁₂

⇒ P = ⁵⁰⁹⁶⁰⁰/₁₁₂

⇒ P = $4550

Thus, the sum borrowed (P) = $4550 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 = 3 years

So, we need to calculate the simple interest for the given time period, which is 3 years

Thus, Simple Interest for 3 years = 3 × Simple Interest for 1 year

= 3 × 4 = 12

Thus, simple interest for 3 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 5096, then the Principal = ¹⁰⁰/₁₁₂ × 5096

= ^{100 × 5096}/₁₁₂

= ⁵⁰⁹⁶⁰⁰/₁₁₂

= 4550

Thus, Principal = $4550

Thus, the sum borrowed = $4550 Answer

Similar Questions

(1) Thomas took a loan of $5600 at the rate of 7% simple interest per annum. If he paid an amount of $8344 to clear the loan, then find the time period of the loan.

(2) In how much time a principal of $3200 will amount to $3488 at a simple interest of 3% per annum?

(3) If Linda borrowed $3350 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.

(4) If Jessica borrowed $3750 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.

(5) Calculate the amount due after 10 years if Susan borrowed a sum of $5650 at a rate of 8% simple interest.

(6) Joseph took a loan of $5400 at the rate of 8% simple interest per annum. If he paid an amount of $7992 to clear the loan, then find the time period of the loan.

(7) Thomas took a loan of $5600 at the rate of 9% simple interest per annum. If he paid an amount of $10640 to clear the loan, then find the time period of the loan.

(8) What amount does John have to pay after 5 years if he takes a loan of $3200 at 4% simple interest?

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

(10) Find the amount to be paid if Karen borrowed a sum of $5950 at 9% simple interest for 7 years.