Simple Interest
Math MCQs

Question :    Linda had to pay $3651.5 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  $3350

Solution & Explanation

Solution

Given,

Amount (A) = $3651.5

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

$3651.5 = P (1 + 3% × 3)

⇒ $3651.5 = P (1 + ³/₁₀₀ × 3)

⇒ $3651.5 = P (1 + ^{3 × 3}/₁₀₀)

⇒ $3651.5 = P (1 + ⁹/₁₀₀)

⇒ $3651.5 = P (^{100 + 9}/₁₀₀)

⇒ $3651.5 = P × ¹⁰⁹/₁₀₀

⇒ P × ¹⁰⁹/₁₀₀ = $3651.5

⇒ P = ^3651.5/_¹⁰⁹/100

⇒ P = 3651.5 × ¹⁰⁰/₁₀₉

⇒ P = ^{3651.5 × 100}/₁₀₉

⇒ P = ³⁶⁵¹⁵⁰/₁₀₉

⇒ P = $3350

Thus, the sum borrowed (P) = $3350 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 3651.5, then the Principal = ¹⁰⁰/₁₀₉ × 3651.5

= ^{100 × 3651.5}/₁₀₉

= ³⁶⁵¹⁵⁰/₁₀₉

= 3350

Thus, Principal = $3350

Thus, the sum borrowed = $3350 Answer

Similar Questions

(1) What amount does Joseph have to pay after 5 years if he takes a loan of $3700 at 9% simple interest?

(2) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 7% simple interest?

(3) How much loan did Kenneth borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8400 to clear it?

(4) Calculate the amount due if Christopher borrowed a sum of $4000 at 6% simple interest for 4 years.

(5) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 10% simple interest for 8 years.

(6) Find the amount to be paid if James borrowed a sum of $5000 at 2% simple interest for 7 years.

(7) Calculate the amount due after 10 years if John borrowed a sum of $5200 at a rate of 6% simple interest.

(8) What amount will be due after 2 years if William borrowed a sum of $3250 at a 6% simple interest?

(9) Jennifer took a loan of $4500 at the rate of 6% simple interest per annum. If he paid an amount of $6390 to clear the loan, then find the time period of the loan.

(10) James took a loan of $4000 at the rate of 10% simple interest per annum. If he paid an amount of $6400 to clear the loan, then find the time period of the loan.