Simple Interest
Math MCQs

Question :    David had to pay $3706 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

Correct Answer  $3400

Solution & Explanation

Solution

Given,

Amount (A) = $3706

Rate of Simple Interest (R) = 3%

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

$3706 = P (1 + 3% × 3)

⇒ $3706 = P (1 + ³/₁₀₀ × 3)

⇒ $3706 = P (1 + ^{3 × 3}/₁₀₀)

⇒ $3706 = P (1 + ⁹/₁₀₀)

⇒ $3706 = P (^{100 + 9}/₁₀₀)

⇒ $3706 = P × ¹⁰⁹/₁₀₀

⇒ P × ¹⁰⁹/₁₀₀ = $3706

⇒ P = ³⁷⁰⁶/_¹⁰⁹/100

⇒ P = 3706 × ¹⁰⁰/₁₀₉

⇒ P = ^{3706 × 100}/₁₀₉

⇒ P = ³⁷⁰⁶⁰⁰/₁₀₉

⇒ P = $3400

Thus, the sum borrowed (P) = $3400 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 = 3% per annum

Thus, Interest = 3% of principal

⇒ Interest = 3% of 100 = 3

Thus, Simple Interest for 1 year = 3

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 × 3 = 9

Thus, simple interest for 3 years = 9

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 9 = 109

Calculation of the Principal

Now,

∵ If the Amount is 109, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₀₉

∴ If the Amount is 3706, then the Principal = ¹⁰⁰/₁₀₉ × 3706

= ^{100 × 3706}/₁₀₉

= ³⁷⁰⁶⁰⁰/₁₀₉

= 3400

Thus, Principal = $3400

Thus, the sum borrowed = $3400 Answer

Similar Questions

(1) If Jessica paid $4500 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(2) What amount does Richard have to pay after 6 years if he takes a loan of $3600 at 3% simple interest?

(3) Susan took a loan of $5300 at the rate of 7% simple interest per annum. If he paid an amount of $7526 to clear the loan, then find the time period of the loan.

(4) Calculate the amount due if Karen borrowed a sum of $3950 at 6% simple interest for 4 years.

(5) Barbara took a loan of $5100 at the rate of 7% simple interest per annum. If he paid an amount of $8670 to clear the loan, then find the time period of the loan.

(6) Betty had to pay $4505 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(7) What amount does Thomas have to pay after 5 years if he takes a loan of $3800 at 10% simple interest?

(8) Calculate the amount due after 10 years if James borrowed a sum of $5000 at a rate of 6% simple interest.

(9) Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 8% simple interest.

(10) Find the amount to be paid if Susan borrowed a sum of $5650 at 6% simple interest for 7 years.