Simple Interest
Math MCQs

Question :    Robert had to pay $3286 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

Correct Answer  $3100

Solution & Explanation

Solution

Given,

Amount (A) = $3286

Rate of Simple Interest (R) = 2%

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

$3286 = P (1 + 2% × 3)

⇒ $3286 = P (1 + ²/₁₀₀ × 3)

⇒ $3286 = P (1 + ^{2 × 3}/₁₀₀)

⇒ $3286 = P (1 + ⁶/₁₀₀)

⇒ $3286 = P (^{100 + 6}/₁₀₀)

⇒ $3286 = P × ¹⁰⁶/₁₀₀

⇒ P × ¹⁰⁶/₁₀₀ = $3286

⇒ P = ³²⁸⁶/_¹⁰⁶/100

⇒ P = 3286 × ¹⁰⁰/₁₀₆

⇒ P = ^{3286 × 100}/₁₀₆

⇒ P = ³²⁸⁶⁰⁰/₁₀₆

⇒ P = $3100

Thus, the sum borrowed (P) = $3100 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 = 2% per annum

Thus, Interest = 2% of principal

⇒ Interest = 2% of 100 = 2

Thus, Simple Interest for 1 year = 2

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 × 2 = 6

Thus, simple interest for 3 years = 6

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 6 = 106

Calculation of the Principal

Now,

∵ If the Amount is 106, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₀₆

∴ If the Amount is 3286, then the Principal = ¹⁰⁰/₁₀₆ × 3286

= ^{100 × 3286}/₁₀₆

= ³²⁸⁶⁰⁰/₁₀₆

= 3100

Thus, Principal = $3100

Thus, the sum borrowed = $3100 Answer

Similar Questions

(1) Elizabeth took a loan of $4900 at the rate of 8% simple interest per annum. If he paid an amount of $7644 to clear the loan, then find the time period of the loan.

(2) Calculate the amount due if Joseph borrowed a sum of $3700 at 2% simple interest for 4 years.

(3) If Steven paid $5336 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(4) Richard took a loan of $5200 at the rate of 8% simple interest per annum. If he paid an amount of $8112 to clear the loan, then find the time period of the loan.

(5) What amount does David have to pay after 6 years if he takes a loan of $3400 at 5% simple interest?

(6) What amount will be due after 2 years if Joshua borrowed a sum of $3950 at a 7% simple interest?

(7) Calculate the amount due if Jessica borrowed a sum of $3750 at 5% simple interest for 3 years.

(8) If Betty paid $4930 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(9) What amount will be due after 2 years if Andrew borrowed a sum of $3900 at a 8% simple interest?

(10) Find the amount to be paid if James borrowed a sum of $5000 at 8% simple interest for 7 years.