Simple Interest
Math MCQs

Question :    How much loan did Anthony borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7875 to clear it?

Correct Answer  $6300

Solution & Explanation

Solution

Given,

Amount (A) = $7875

Rate of Simple Interest (R) = 5%

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

$7875 = P (1 + 5% × 5)

⇒ $7875 = P (1 + ⁵/₁₀₀ × 5)

⇒ $7875 = P (1 + ^{5 × 5}/₁₀₀)

⇒ $7875 = P (1 + ²⁵/₁₀₀)

⇒ $7875 = P (^{100 + 25}/₁₀₀)

⇒ $7875 = P × ¹²⁵/₁₀₀

⇒ P × ¹²⁵/₁₀₀ = $7875

⇒ P = ⁷⁸⁷⁵/_¹²⁵/100

⇒ P = 7875 × ¹⁰⁰/₁₂₅

⇒ P = ^{7875 × 100}/₁₂₅

⇒ P = ⁷⁸⁷⁵⁰⁰/₁₂₅

⇒ P = $6300

Thus, the sum borrowed (P) = $6300 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 = 5% per annum

Thus, Interest = 5% of principal

⇒ Interest = 5% of 100 = 5

Thus, Simple Interest for 1 year = 5

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 × 5 = 25

Thus, simple interest for 5 years = 25

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 25 = 125

Calculation of the Principal

Now,

∵ If the Amount is 125, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₂₅

∴ If the Amount is 7875, then the Principal = ¹⁰⁰/₁₂₅ × 7875

= ^{100 × 7875}/₁₂₅

= ⁷⁸⁷⁵⁰⁰/₁₂₅

= 6300

Thus, Principal = $6300

Thus, the sum borrowed = $6300 Answer

Similar Questions

(1) Betty took a loan of $6500 at the rate of 10% simple interest per annum. If he paid an amount of $11700 to clear the loan, then find the time period of the loan.

(2) If Jennifer paid $3770 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(3) Calculate the amount due if Joseph borrowed a sum of $3700 at 6% simple interest for 3 years.

(4) If Susan paid $4234 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(5) Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 7% simple interest.

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

(7) What amount will be due after 2 years if Steven borrowed a sum of $3800 at a 8% simple interest?

(8) How much loan did Richard borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7000 to clear it?

(9) What amount will be due after 2 years if Thomas borrowed a sum of $3400 at a 7% simple interest?

(10) Nancy took a loan of $6300 at the rate of 6% simple interest per annum. If he paid an amount of $8946 to clear the loan, then find the time period of the loan.