Simple Interest
Math MCQs

Question :    Jennifer had to pay $3542.5 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  $3250

Solution & Explanation

Solution

Given,

Amount (A) = $3542.5

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

$3542.5 = P (1 + 3% × 3)

⇒ $3542.5 = P (1 + ³/₁₀₀ × 3)

⇒ $3542.5 = P (1 + ^{3 × 3}/₁₀₀)

⇒ $3542.5 = P (1 + ⁹/₁₀₀)

⇒ $3542.5 = P (^{100 + 9}/₁₀₀)

⇒ $3542.5 = P × ¹⁰⁹/₁₀₀

⇒ P × ¹⁰⁹/₁₀₀ = $3542.5

⇒ P = ^3542.5/_¹⁰⁹/100

⇒ P = 3542.5 × ¹⁰⁰/₁₀₉

⇒ P = ^{3542.5 × 100}/₁₀₉

⇒ P = ³⁵⁴²⁵⁰/₁₀₉

⇒ P = $3250

Thus, the sum borrowed (P) = $3250 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 3542.5, then the Principal = ¹⁰⁰/₁₀₉ × 3542.5

= ^{100 × 3542.5}/₁₀₉

= ³⁵⁴²⁵⁰/₁₀₉

= 3250

Thus, Principal = $3250

Thus, the sum borrowed = $3250 Answer

Similar Questions

(1) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 8% simple interest for 7 years.

(2) What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 6% simple interest?

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

(4) What amount will be due after 2 years if Daniel borrowed a sum of $3550 at a 5% simple interest?

(5) 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.

(6) In how much time a principal of $3050 will amount to $3538 at a simple interest of 4% per annum?

(7) Find the amount to be paid if John borrowed a sum of $5200 at 5% simple interest for 8 years.

(8) Find the amount to be paid if Charles borrowed a sum of $5900 at 5% simple interest for 8 years.

(9) Jessica took a loan of $5500 at the rate of 6% simple interest per annum. If he paid an amount of $7810 to clear the loan, then find the time period of the loan.

(10) Thomas took a loan of $5600 at the rate of 7% simple interest per annum. If he paid an amount of $8736 to clear the loan, then find the time period of the loan.