Simple Interest
Math MCQs

Question :    How much loan did Ronald borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8250 to clear it?

Correct Answer  $7500

Solution & Explanation

Solution

Given,

Amount (A) = $8250

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

$8250 = P (1 + 2% × 5)

⇒ $8250 = P (1 + ²/₁₀₀ × 5)

⇒ $8250 = P (1 + ^{2 × 5}/₁₀₀)

⇒ $8250 = P (1 + ¹⁰/₁₀₀)

⇒ $8250 = P (^{100 + 10}/₁₀₀)

⇒ $8250 = P × ¹¹⁰/₁₀₀

⇒ P × ¹¹⁰/₁₀₀ = $8250

⇒ P = ⁸²⁵⁰/_¹¹⁰/100

⇒ P = 8250 × ¹⁰⁰/₁₁₀

⇒ P = ^{8250 × 100}/₁₁₀

⇒ P = ⁸²⁵⁰⁰⁰/₁₁₀

⇒ P = $7500

Thus, the sum borrowed (P) = $7500 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 8250, then the Principal = ¹⁰⁰/₁₁₀ × 8250

= ^{100 × 8250}/₁₁₀

= ⁸²⁵⁰⁰⁰/₁₁₀

= 7500

Thus, Principal = $7500

Thus, the sum borrowed = $7500 Answer

Similar Questions

(1) Find the amount to be paid if Mary borrowed a sum of $5050 at 7% simple interest for 8 years.

(2) How much loan did Edward borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9120 to clear it?

(3) Calculate the amount due if Joseph borrowed a sum of $3700 at 7% simple interest for 3 years.

(4) Calculate the amount due after 9 years if Jennifer borrowed a sum of $5250 at a rate of 4% simple interest.

(5) Find the amount to be paid if Joseph borrowed a sum of $5700 at 9% simple interest for 8 years.

(6) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 3% simple interest for 3 years.

(7) Calculate the amount due if Richard borrowed a sum of $3600 at 5% simple interest for 4 years.

(8) How much loan did David borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6480 to clear it?

(9) What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 8% simple interest?

(10) Robert took a loan of $4200 at the rate of 9% simple interest per annum. If he paid an amount of $6846 to clear the loan, then find the time period of the loan.