Simple Interest
Math MCQs

Question :    Sandra had to pay $4850.5 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  $4450

Solution & Explanation

Solution

Given,

Amount (A) = $4850.5

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

$4850.5 = P (1 + 3% × 3)

⇒ $4850.5 = P (1 + ³/₁₀₀ × 3)

⇒ $4850.5 = P (1 + ^{3 × 3}/₁₀₀)

⇒ $4850.5 = P (1 + ⁹/₁₀₀)

⇒ $4850.5 = P (^{100 + 9}/₁₀₀)

⇒ $4850.5 = P × ¹⁰⁹/₁₀₀

⇒ P × ¹⁰⁹/₁₀₀ = $4850.5

⇒ P = ^4850.5/_¹⁰⁹/100

⇒ P = 4850.5 × ¹⁰⁰/₁₀₉

⇒ P = ^{4850.5 × 100}/₁₀₉

⇒ P = ⁴⁸⁵⁰⁵⁰/₁₀₉

⇒ P = $4450

Thus, the sum borrowed (P) = $4450 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 4850.5, then the Principal = ¹⁰⁰/₁₀₉ × 4850.5

= ^{100 × 4850.5}/₁₀₉

= ⁴⁸⁵⁰⁵⁰/₁₀₉

= 4450

Thus, Principal = $4450

Thus, the sum borrowed = $4450 Answer

Similar Questions

(1) In how much time a principal of $3150 will amount to $3528 at a simple interest of 4% per annum?

(2) Find the amount to be paid if Linda borrowed a sum of $5350 at 5% simple interest for 7 years.

(3) Susan took a loan of $5300 at the rate of 8% simple interest per annum. If he paid an amount of $8268 to clear the loan, then find the time period of the loan.

(4) Michael took a loan of $4600 at the rate of 8% simple interest per annum. If he paid an amount of $7912 to clear the loan, then find the time period of the loan.

(5) Find the amount to be paid if Michael borrowed a sum of $5300 at 6% simple interest for 7 years.

(6) What amount will be due after 2 years if Kenneth borrowed a sum of $4000 at a 8% simple interest?

(7) Calculate the amount due after 10 years if Susan borrowed a sum of $5650 at a rate of 8% simple interest.

(8) Donald took a loan of $7000 at the rate of 9% simple interest per annum. If he paid an amount of $12670 to clear the loan, then find the time period of the loan.

(9) Lisa had to pay $4657.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(10) Find the amount to be paid if Karen borrowed a sum of $5950 at 2% simple interest for 8 years.