Simple Interest
Math MCQs

Question :    Susan had to pay $3978.5 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  $3650

Solution & Explanation

Solution

Given,

Amount (A) = $3978.5

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

$3978.5 = P (1 + 3% × 3)

⇒ $3978.5 = P (1 + ³/₁₀₀ × 3)

⇒ $3978.5 = P (1 + ^{3 × 3}/₁₀₀)

⇒ $3978.5 = P (1 + ⁹/₁₀₀)

⇒ $3978.5 = P (^{100 + 9}/₁₀₀)

⇒ $3978.5 = P × ¹⁰⁹/₁₀₀

⇒ P × ¹⁰⁹/₁₀₀ = $3978.5

⇒ P = ^3978.5/_¹⁰⁹/100

⇒ P = 3978.5 × ¹⁰⁰/₁₀₉

⇒ P = ^{3978.5 × 100}/₁₀₉

⇒ P = ³⁹⁷⁸⁵⁰/₁₀₉

⇒ P = $3650

Thus, the sum borrowed (P) = $3650 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 3978.5, then the Principal = ¹⁰⁰/₁₀₉ × 3978.5

= ^{100 × 3978.5}/₁₀₉

= ³⁹⁷⁸⁵⁰/₁₀₉

= 3650

Thus, Principal = $3650

Thus, the sum borrowed = $3650 Answer

Similar Questions

(1) Richard had to pay $3816 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(2) Daniel took a loan of $6200 at the rate of 10% simple interest per annum. If he paid an amount of $12400 to clear the loan, then find the time period of the loan.

(3) Nancy took a loan of $6300 at the rate of 7% simple interest per annum. If he paid an amount of $10269 to clear the loan, then find the time period of the loan.

(4) Calculate the amount due if William borrowed a sum of $3500 at 6% simple interest for 4 years.

(5) What amount will be due after 2 years if Joseph borrowed a sum of $3350 at a 9% simple interest?

(6) If Daniel paid $4756 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(7) What amount does Linda have to pay after 6 years if he takes a loan of $3350 at 2% simple interest?

(8) What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 9% simple interest?

(9) Robert took a loan of $4200 at the rate of 9% simple interest per annum. If he paid an amount of $7602 to clear the loan, then find the time period of the loan.

(10) What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 4% simple interest?