Simple Interest
Math MCQs

Question :    William had to pay $3710 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  $3500

Solution & Explanation

Solution

Given,

Amount (A) = $3710

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

$3710 = P (1 + 2% × 3)

⇒ $3710 = P (1 + ²/₁₀₀ × 3)

⇒ $3710 = P (1 + ^{2 × 3}/₁₀₀)

⇒ $3710 = P (1 + ⁶/₁₀₀)

⇒ $3710 = P (^{100 + 6}/₁₀₀)

⇒ $3710 = P × ¹⁰⁶/₁₀₀

⇒ P × ¹⁰⁶/₁₀₀ = $3710

⇒ P = ³⁷¹⁰/_¹⁰⁶/100

⇒ P = 3710 × ¹⁰⁰/₁₀₆

⇒ P = ^{3710 × 100}/₁₀₆

⇒ P = ³⁷¹⁰⁰⁰/₁₀₆

⇒ P = $3500

Thus, the sum borrowed (P) = $3500 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 3710, then the Principal = ¹⁰⁰/₁₀₆ × 3710

= ^{100 × 3710}/₁₀₆

= ³⁷¹⁰⁰⁰/₁₀₆

= 3500

Thus, Principal = $3500

Thus, the sum borrowed = $3500 Answer

Similar Questions

(1) What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 10% simple interest?

(2) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 8% simple interest for 7 years.

(3) How much loan did John borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $5980 to clear it?

(4) Find the amount to be paid if Charles borrowed a sum of $5900 at 2% simple interest for 7 years.

(5) Calculate the amount due if Linda borrowed a sum of $3350 at 10% simple interest for 4 years.

(6) Calculate the amount due if Sarah borrowed a sum of $3850 at 9% simple interest for 3 years.

(7) If William paid $4200 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(8) Donald had to pay $4905 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(9) Charles took a loan of $5800 at the rate of 6% simple interest per annum. If he paid an amount of $9280 to clear the loan, then find the time period of the loan.

(10) Calculate the amount due after 10 years if Charles borrowed a sum of $5900 at a rate of 6% simple interest.