Simple Interest
Math MCQs

Question :    How much loan did Amanda borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7865 to clear it?

Correct Answer  $7150

Solution & Explanation

Solution

Given,

Amount (A) = $7865

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

$7865 = P (1 + 2% × 5)

⇒ $7865 = P (1 + ²/₁₀₀ × 5)

⇒ $7865 = P (1 + ^{2 × 5}/₁₀₀)

⇒ $7865 = P (1 + ¹⁰/₁₀₀)

⇒ $7865 = P (^{100 + 10}/₁₀₀)

⇒ $7865 = P × ¹¹⁰/₁₀₀

⇒ P × ¹¹⁰/₁₀₀ = $7865

⇒ P = ⁷⁸⁶⁵/_¹¹⁰/100

⇒ P = 7865 × ¹⁰⁰/₁₁₀

⇒ P = ^{7865 × 100}/₁₁₀

⇒ P = ⁷⁸⁶⁵⁰⁰/₁₁₀

⇒ P = $7150

Thus, the sum borrowed (P) = $7150 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 7865, then the Principal = ¹⁰⁰/₁₁₀ × 7865

= ^{100 × 7865}/₁₁₀

= ⁷⁸⁶⁵⁰⁰/₁₁₀

= 7150

Thus, Principal = $7150

Thus, the sum borrowed = $7150 Answer

Similar Questions

(1) Lisa took a loan of $6100 at the rate of 8% simple interest per annum. If he paid an amount of $10492 to clear the loan, then find the time period of the loan.

(2) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 4% simple interest?

(3) Calculate the amount due after 10 years if Barbara borrowed a sum of $5550 at a rate of 7% simple interest.

(4) Find the amount to be paid if Sarah borrowed a sum of $5850 at 7% simple interest for 7 years.

(5) Christopher took a loan of $6000 at the rate of 6% simple interest per annum. If he paid an amount of $9600 to clear the loan, then find the time period of the loan.

(6) Jessica took a loan of $5500 at the rate of 10% simple interest per annum. If he paid an amount of $9350 to clear the loan, then find the time period of the loan.

(7) Richard took a loan of $5200 at the rate of 10% simple interest per annum. If he paid an amount of $9880 to clear the loan, then find the time period of the loan.

(8) What amount will be due after 2 years if Mark borrowed a sum of $3700 at a 8% simple interest?

(9) What amount does Linda have to pay after 6 years if he takes a loan of $3350 at 9% simple interest?

(10) Christopher took a loan of $6000 at the rate of 7% simple interest per annum. If he paid an amount of $9780 to clear the loan, then find the time period of the loan.