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) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 8% simple interest?

(2) Find the amount to be paid if Christopher borrowed a sum of $6000 at 9% simple interest for 7 years.

(3) Find the amount to be paid if Michael borrowed a sum of $5300 at 2% simple interest for 8 years.

(4) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 2% simple interest?

(5) Mark took a loan of $6800 at the rate of 9% simple interest per annum. If he paid an amount of $12920 to clear the loan, then find the time period of the loan.

(6) Calculate the amount due after 9 years if Michael borrowed a sum of $5300 at a rate of 2% simple interest.

(7) In how much time a principal of $3050 will amount to $3660 at a simple interest of 4% per annum?

(8) Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 2% simple interest.

(9) In how much time a principal of $3200 will amount to $3680 at a simple interest of 5% per annum?

(10) Calculate the amount due if Susan borrowed a sum of $3650 at 7% simple interest for 3 years.