Simple Interest
Math MCQs

Question :    Elizabeth had to pay $3760.5 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  $3450

Solution & Explanation

Solution

Given,

Amount (A) = $3760.5

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

$3760.5 = P (1 + 3% × 3)

⇒ $3760.5 = P (1 + ³/₁₀₀ × 3)

⇒ $3760.5 = P (1 + ^{3 × 3}/₁₀₀)

⇒ $3760.5 = P (1 + ⁹/₁₀₀)

⇒ $3760.5 = P (^{100 + 9}/₁₀₀)

⇒ $3760.5 = P × ¹⁰⁹/₁₀₀

⇒ P × ¹⁰⁹/₁₀₀ = $3760.5

⇒ P = ^3760.5/_¹⁰⁹/100

⇒ P = 3760.5 × ¹⁰⁰/₁₀₉

⇒ P = ^{3760.5 × 100}/₁₀₉

⇒ P = ³⁷⁶⁰⁵⁰/₁₀₉

⇒ P = $3450

Thus, the sum borrowed (P) = $3450 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 3760.5, then the Principal = ¹⁰⁰/₁₀₉ × 3760.5

= ^{100 × 3760.5}/₁₀₉

= ³⁷⁶⁰⁵⁰/₁₀₉

= 3450

Thus, Principal = $3450

Thus, the sum borrowed = $3450 Answer

Similar Questions

(1) What amount will be due after 2 years if Mark borrowed a sum of $3700 at a 9% simple interest?

(2) 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.

(3) Daniel took a loan of $6200 at the rate of 6% simple interest per annum. If he paid an amount of $9548 to clear the loan, then find the time period of the loan.

(4) Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 3% simple interest.

(5) Find the amount to be paid if Karen borrowed a sum of $5950 at 4% simple interest for 7 years.

(6) Calculate the amount due if Robert borrowed a sum of $3100 at 6% simple interest for 3 years.

(7) How much loan did Barbara borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6660 to clear it?

(8) Calculate the amount due after 10 years if Sarah borrowed a sum of $5850 at a rate of 2% simple interest.

(9) Find the amount to be paid if Barbara borrowed a sum of $5550 at 8% simple interest for 7 years.

(10) Calculate the amount due if Robert borrowed a sum of $3100 at 4% simple interest for 4 years.