Simple Interest
Math MCQs

Question :    Susan had to pay $3869 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

Correct Answer  $3650

Solution & Explanation

Solution

Given,

Amount (A) = $3869

Rate of Simple Interest (R) = 2%

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

$3869 = P (1 + 2% × 3)

⇒ $3869 = P (1 + ²/₁₀₀ × 3)

⇒ $3869 = P (1 + ^{2 × 3}/₁₀₀)

⇒ $3869 = P (1 + ⁶/₁₀₀)

⇒ $3869 = P (^{100 + 6}/₁₀₀)

⇒ $3869 = P × ¹⁰⁶/₁₀₀

⇒ P × ¹⁰⁶/₁₀₀ = $3869

⇒ P = ³⁸⁶⁹/_¹⁰⁶/100

⇒ P = 3869 × ¹⁰⁰/₁₀₆

⇒ P = ^{3869 × 100}/₁₀₆

⇒ P = ³⁸⁶⁹⁰⁰/₁₀₆

⇒ P = $3650

Thus, the sum borrowed (P) = $3650 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 = 2% per annum

Thus, Interest = 2% of principal

⇒ Interest = 2% of 100 = 2

Thus, Simple Interest for 1 year = 2

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 × 2 = 6

Thus, simple interest for 3 years = 6

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 6 = 106

Calculation of the Principal

Now,

∵ If the Amount is 106, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₀₆

∴ If the Amount is 3869, then the Principal = ¹⁰⁰/₁₀₆ × 3869

= ^{100 × 3869}/₁₀₆

= ³⁸⁶⁹⁰⁰/₁₀₆

= 3650

Thus, Principal = $3650

Thus, the sum borrowed = $3650 Answer

Similar Questions

(1) In how much time a principal of $3000 will amount to $3600 at a simple interest of 4% per annum?

(2) In how much time a principal of $3000 will amount to $3300 at a simple interest of 2% per annum?

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

(4) David took a loan of $4800 at the rate of 10% simple interest per annum. If he paid an amount of $9600 to clear the loan, then find the time period of the loan.

(5) How much loan did Jessica borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6612.5 to clear it?

(6) Calculate the amount due after 9 years if Robert borrowed a sum of $5100 at a rate of 6% simple interest.

(7) Donald took a loan of $7000 at the rate of 8% simple interest per annum. If he paid an amount of $10360 to clear the loan, then find the time period of the loan.

(8) If Elizabeth borrowed $3450 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.

(9) What amount does Barbara have to pay after 5 years if he takes a loan of $3550 at 10% simple interest?

(10) Calculate the amount due if Jessica borrowed a sum of $3750 at 10% simple interest for 4 years.