Simple Interest
Math MCQs

Question :    Sarah had to pay $4196.5 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  $3850

Solution & Explanation

Solution

Given,

Amount (A) = $4196.5

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

$4196.5 = P (1 + 3% × 3)

⇒ $4196.5 = P (1 + ³/₁₀₀ × 3)

⇒ $4196.5 = P (1 + ^{3 × 3}/₁₀₀)

⇒ $4196.5 = P (1 + ⁹/₁₀₀)

⇒ $4196.5 = P (^{100 + 9}/₁₀₀)

⇒ $4196.5 = P × ¹⁰⁹/₁₀₀

⇒ P × ¹⁰⁹/₁₀₀ = $4196.5

⇒ P = ^4196.5/_¹⁰⁹/100

⇒ P = 4196.5 × ¹⁰⁰/₁₀₉

⇒ P = ^{4196.5 × 100}/₁₀₉

⇒ P = ⁴¹⁹⁶⁵⁰/₁₀₉

⇒ P = $3850

Thus, the sum borrowed (P) = $3850 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 4196.5, then the Principal = ¹⁰⁰/₁₀₉ × 4196.5

= ^{100 × 4196.5}/₁₀₉

= ⁴¹⁹⁶⁵⁰/₁₀₉

= 3850

Thus, Principal = $3850

Thus, the sum borrowed = $3850 Answer

Similar Questions

(1) Find the amount to be paid if Sarah borrowed a sum of $5850 at 9% simple interest for 8 years.

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

(3) If Michelle paid $5940 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(4) What amount does Jennifer have to pay after 6 years if he takes a loan of $3250 at 2% simple interest?

(5) Calculate the amount due after 10 years if Richard borrowed a sum of $5600 at a rate of 6% simple interest.

(6) Calculate the amount due if Linda borrowed a sum of $3350 at 2% simple interest for 3 years.

(7) What amount will be due after 2 years if Joshua borrowed a sum of $3950 at a 9% simple interest?

(8) If Mark paid $5280 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(9) Nancy took a loan of $6300 at the rate of 9% simple interest per annum. If he paid an amount of $9702 to clear the loan, then find the time period of the loan.

(10) Matthew took a loan of $6400 at the rate of 10% simple interest per annum. If he paid an amount of $12800 to clear the loan, then find the time period of the loan.