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) What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 7% simple interest?

(2) Matthew took a loan of $6400 at the rate of 9% simple interest per annum. If he paid an amount of $10432 to clear the loan, then find the time period of the loan.

(3) Calculate the amount due if Barbara borrowed a sum of $3550 at 9% simple interest for 4 years.

(4) Lisa took a loan of $6100 at the rate of 9% simple interest per annum. If he paid an amount of $9943 to clear the loan, then find the time period of the loan.

(5) Calculate the amount due after 10 years if John borrowed a sum of $5200 at a rate of 3% simple interest.

(6) Find the amount to be paid if James borrowed a sum of $5000 at 3% simple interest for 7 years.

(7) What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 7% simple interest?

(8) Donald took a loan of $7000 at the rate of 8% simple interest per annum. If he paid an amount of $12040 to clear the loan, then find the time period of the loan.

(9) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 5% simple interest for 8 years.

(10) How much loan did Susan borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6780 to clear it?