Simple Interest
Math MCQs

Question :    How much loan did Edward borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8360 to clear it?

Correct Answer  $7600

Solution & Explanation

Solution

Given,

Amount (A) = $8360

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

$8360 = P (1 + 2% × 5)

⇒ $8360 = P (1 + ²/₁₀₀ × 5)

⇒ $8360 = P (1 + ^{2 × 5}/₁₀₀)

⇒ $8360 = P (1 + ¹⁰/₁₀₀)

⇒ $8360 = P (^{100 + 10}/₁₀₀)

⇒ $8360 = P × ¹¹⁰/₁₀₀

⇒ P × ¹¹⁰/₁₀₀ = $8360

⇒ P = ⁸³⁶⁰/_¹¹⁰/100

⇒ P = 8360 × ¹⁰⁰/₁₁₀

⇒ P = ^{8360 × 100}/₁₁₀

⇒ P = ⁸³⁶⁰⁰⁰/₁₁₀

⇒ P = $7600

Thus, the sum borrowed (P) = $7600 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 8360, then the Principal = ¹⁰⁰/₁₁₀ × 8360

= ^{100 × 8360}/₁₁₀

= ⁸³⁶⁰⁰⁰/₁₁₀

= 7600

Thus, Principal = $7600

Thus, the sum borrowed = $7600 Answer

Similar Questions

(1) What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 6% simple interest?

(2) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 8% simple interest?

(3) 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.

(4) Calculate the amount due if Karen borrowed a sum of $3950 at 8% simple interest for 4 years.

(5) Barbara took a loan of $5100 at the rate of 9% simple interest per annum. If he paid an amount of $9231 to clear the loan, then find the time period of the loan.

(6) Sarah had to pay $4196.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(7) Find the amount to be paid if Thomas borrowed a sum of $5800 at 3% simple interest for 8 years.

(8) Calculate the amount due after 10 years if Joseph borrowed a sum of $5700 at a rate of 2% simple interest.

(9) James took a loan of $4000 at the rate of 7% simple interest per annum. If he paid an amount of $6520 to clear the loan, then find the time period of the loan.

(10) In how much time a principal of $3000 will amount to $3180 at a simple interest of 3% per annum?