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) Sandra took a loan of $6900 at the rate of 7% simple interest per annum. If he paid an amount of $10764 to clear the loan, then find the time period of the loan.

(2) Mary took a loan of $4100 at the rate of 8% simple interest per annum. If he paid an amount of $7380 to clear the loan, then find the time period of the loan.

(3) Mark took a loan of $6800 at the rate of 10% simple interest per annum. If he paid an amount of $12920 to clear the loan, then find the time period of the loan.

(4) In how much time a principal of $3150 will amount to $3780 at a simple interest of 4% per annum?

(5) Matthew took a loan of $6400 at the rate of 7% simple interest per annum. If he paid an amount of $10432 to clear the loan, then find the time period of the loan.

(6) Emily had to pay $5035 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(7) Calculate the amount due if Linda borrowed a sum of $3350 at 7% simple interest for 3 years.

(8) Barbara took a loan of $5100 at the rate of 8% simple interest per annum. If he paid an amount of $8364 to clear the loan, then find the time period of the loan.

(9) Joseph took a loan of $5400 at the rate of 10% simple interest per annum. If he paid an amount of $10800 to clear the loan, then find the time period of the loan.

(10) Find the amount to be paid if Susan borrowed a sum of $5650 at 3% simple interest for 7 years.