Simple Interest
Math MCQs

Question :    Joshua had to pay $5488 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  $4900

Solution & Explanation

Solution

Given,

Amount (A) = $5488

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

$5488 = P (1 + 4% × 3)

⇒ $5488 = P (1 + ⁴/₁₀₀ × 3)

⇒ $5488 = P (1 + ^{4 × 3}/₁₀₀)

⇒ $5488 = P (1 + ¹²/₁₀₀)

⇒ $5488 = P (^{100 + 12}/₁₀₀)

⇒ $5488 = P × ¹¹²/₁₀₀

⇒ P × ¹¹²/₁₀₀ = $5488

⇒ P = ⁵⁴⁸⁸/_¹¹²/100

⇒ P = 5488 × ¹⁰⁰/₁₁₂

⇒ P = ^{5488 × 100}/₁₁₂

⇒ P = ⁵⁴⁸⁸⁰⁰/₁₁₂

⇒ P = $4900

Thus, the sum borrowed (P) = $4900 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 5488, then the Principal = ¹⁰⁰/₁₁₂ × 5488

= ^{100 × 5488}/₁₁₂

= ⁵⁴⁸⁸⁰⁰/₁₁₂

= 4900

Thus, Principal = $4900

Thus, the sum borrowed = $4900 Answer

Similar Questions

(1) Charles took a loan of $5800 at the rate of 7% simple interest per annum. If he paid an amount of $9860 to clear the loan, then find the time period of the loan.

(2) David took a loan of $4800 at the rate of 10% simple interest per annum. If he paid an amount of $8640 to clear the loan, then find the time period of the loan.

(3) Richard took a loan of $5200 at the rate of 7% simple interest per annum. If he paid an amount of $8840 to clear the loan, then find the time period of the loan.

(4) What amount will be due after 2 years if Steven borrowed a sum of $3800 at a 4% simple interest?

(5) Calculate the amount due after 10 years if Jessica borrowed a sum of $5750 at a rate of 5% simple interest.

(6) Calculate the amount due if Barbara borrowed a sum of $3550 at 8% simple interest for 3 years.

(7) What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 4% simple interest?

(8) Find the amount to be paid if Joseph borrowed a sum of $5700 at 2% simple interest for 7 years.

(9) Linda took a loan of $4700 at the rate of 6% simple interest per annum. If he paid an amount of $6392 to clear the loan, then find the time period of the loan.

(10) Calculate the amount due if Joseph borrowed a sum of $3700 at 6% simple interest for 4 years.