Simple Interest
Math MCQs

Question :    How much loan did Steven borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7260 to clear it?

Correct Answer  $6600

Solution & Explanation

Solution

Given,

Amount (A) = $7260

Rate of Simple Interest (R) = 2%

Time (T) = 5 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

$7260 = P (1 + 2% × 5)

⇒ $7260 = P (1 + ²/₁₀₀ × 5)

⇒ $7260 = P (1 + ^{2 × 5}/₁₀₀)

⇒ $7260 = P (1 + ¹⁰/₁₀₀)

⇒ $7260 = P (^{100 + 10}/₁₀₀)

⇒ $7260 = P × ¹¹⁰/₁₀₀

⇒ P × ¹¹⁰/₁₀₀ = $7260

⇒ P = ⁷²⁶⁰/_¹¹⁰/100

⇒ P = 7260 × ¹⁰⁰/₁₁₀

⇒ P = ^{7260 × 100}/₁₁₀

⇒ P = ⁷²⁶⁰⁰⁰/₁₁₀

⇒ P = $6600

Thus, the sum borrowed (P) = $6600 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 = 5 years

So, we need to calculate the simple interest for the given time period, which is 5 years

Thus, Simple Interest for 5 years = 5 × Simple Interest for 1 year

= 5 × 2 = 10

Thus, simple interest for 5 years = 10

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 10 = 110

Calculation of the Principal

Now,

∵ If the Amount is 110, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₁₀

∴ If the Amount is 7260, then the Principal = ¹⁰⁰/₁₁₀ × 7260

= ^{100 × 7260}/₁₁₀

= ⁷²⁶⁰⁰⁰/₁₁₀

= 6600

Thus, Principal = $6600

Thus, the sum borrowed = $6600 Answer

Similar Questions

(1) Charles took a loan of $5800 at the rate of 10% simple interest per annum. If he paid an amount of $10440 to clear the loan, then find the time period of the loan.

(2) How much loan did Nancy borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7072.5 to clear it?

(3) Kimberly had to pay $5068.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(4) How much loan did Stephanie borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8682.5 to clear it?

(5) Margaret took a loan of $6700 at the rate of 7% simple interest per annum. If he paid an amount of $10452 to clear the loan, then find the time period of the loan.

(6) In how much time a principal of $3000 will amount to $3360 at a simple interest of 3% per annum?

(7) Find the amount to be paid if Susan borrowed a sum of $5650 at 9% simple interest for 7 years.

(8) Calculate the amount due after 9 years if Sarah borrowed a sum of $5850 at a rate of 6% simple interest.

(9) Paul had to pay $4982 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(10) Joseph took a loan of $5400 at the rate of 6% simple interest per annum. If he paid an amount of $8316 to clear the loan, then find the time period of the loan.