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) Thomas took a loan of $5600 at the rate of 6% simple interest per annum. If he paid an amount of $7952 to clear the loan, then find the time period of the loan.

(2) Find the amount to be paid if Barbara borrowed a sum of $5550 at 7% simple interest for 7 years.

(3) Calculate the amount due if Jessica borrowed a sum of $3750 at 2% simple interest for 3 years.

(4) How much loan did Cynthia borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8745 to clear it?

(5) Richard took a loan of $5200 at the rate of 6% simple interest per annum. If he paid an amount of $7696 to clear the loan, then find the time period of the loan.

(6) Find the amount to be paid if Patricia borrowed a sum of $5150 at 5% simple interest for 8 years.

(7) Calculate the amount due if Susan borrowed a sum of $3650 at 4% simple interest for 3 years.

(8) What amount does Barbara have to pay after 6 years if he takes a loan of $3550 at 7% simple interest?

(9) If James borrowed $3000 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.

(10) Calculate the amount due if Charles borrowed a sum of $3900 at 2% simple interest for 4 years.