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) What amount will be due after 2 years if Mark borrowed a sum of $3700 at a 5% simple interest?

(2) Calculate the amount due after 10 years if Michael borrowed a sum of $5300 at a rate of 2% simple interest.

(3) What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 4% simple interest?

(4) If Nancy paid $4482 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(5) What amount will be due after 2 years if Christopher borrowed a sum of $3500 at a 8% simple interest?

(6) Calculate the amount due after 10 years if Sarah borrowed a sum of $5850 at a rate of 7% simple interest.

(7) James took a loan of $4000 at the rate of 6% simple interest per annum. If he paid an amount of $5920 to clear the loan, then find the time period of the loan.

(8) Calculate the amount due after 9 years if Linda borrowed a sum of $5350 at a rate of 3% simple interest.

(9) Mary took a loan of $4100 at the rate of 8% simple interest per annum. If he paid an amount of $7380 to clear the loan, then find the time period of the loan.

(10) Calculate the amount due after 10 years if John borrowed a sum of $5200 at a rate of 2% simple interest.