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) Karen took a loan of $5900 at the rate of 6% simple interest per annum. If he paid an amount of $9086 to clear the loan, then find the time period of the loan.

(2) Calculate the amount due if Karen borrowed a sum of $3950 at 8% simple interest for 3 years.

(3) Find the amount to be paid if Christopher borrowed a sum of $6000 at 4% simple interest for 8 years.

(4) Calculate the amount due if Susan borrowed a sum of $3650 at 6% simple interest for 3 years.

(5) What amount does John have to pay after 5 years if he takes a loan of $3200 at 5% simple interest?

(6) Calculate the amount due after 10 years if Mary borrowed a sum of $5050 at a rate of 4% simple interest.

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

(8) Patricia took a loan of $4300 at the rate of 6% simple interest per annum. If he paid an amount of $6106 to clear the loan, then find the time period of the loan.

(9) Sarah took a loan of $5700 at the rate of 6% simple interest per annum. If he paid an amount of $9120 to clear the loan, then find the time period of the loan.

(10) Sarah took a loan of $5700 at the rate of 10% simple interest per annum. If he paid an amount of $9120 to clear the loan, then find the time period of the loan.