Simple Interest
Math MCQs

Question :    How much loan did Donald borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7150 to clear it?

Correct Answer  $6500

Solution & Explanation

Solution

Given,

Amount (A) = $7150

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

$7150 = P (1 + 2% × 5)

⇒ $7150 = P (1 + ²/₁₀₀ × 5)

⇒ $7150 = P (1 + ^{2 × 5}/₁₀₀)

⇒ $7150 = P (1 + ¹⁰/₁₀₀)

⇒ $7150 = P (^{100 + 10}/₁₀₀)

⇒ $7150 = P × ¹¹⁰/₁₀₀

⇒ P × ¹¹⁰/₁₀₀ = $7150

⇒ P = ⁷¹⁵⁰/_¹¹⁰/100

⇒ P = 7150 × ¹⁰⁰/₁₁₀

⇒ P = ^{7150 × 100}/₁₁₀

⇒ P = ⁷¹⁵⁰⁰⁰/₁₁₀

⇒ P = $6500

Thus, the sum borrowed (P) = $6500 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 7150, then the Principal = ¹⁰⁰/₁₁₀ × 7150

= ^{100 × 7150}/₁₁₀

= ⁷¹⁵⁰⁰⁰/₁₁₀

= 6500

Thus, Principal = $6500

Thus, the sum borrowed = $6500 Answer

Similar Questions

(1) What amount will be due after 2 years if Joshua borrowed a sum of $3950 at a 5% simple interest?

(2) What amount does Richard have to pay after 6 years if he takes a loan of $3600 at 4% simple interest?

(3) Calculate the amount due if William borrowed a sum of $3500 at 8% simple interest for 3 years.

(4) Find the amount to be paid if Jessica borrowed a sum of $5750 at 4% simple interest for 7 years.

(5) Donald had to pay $4770 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(6) Margaret took a loan of $6700 at the rate of 10% simple interest per annum. If he paid an amount of $12730 to clear the loan, then find the time period of the loan.

(7) How much loan did Joshua borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8625 to clear it?

(8) Linda took a loan of $4700 at the rate of 6% simple interest per annum. If he paid an amount of $6956 to clear the loan, then find the time period of the loan.

(9) Patricia took a loan of $4300 at the rate of 6% simple interest per annum. If he paid an amount of $5848 to clear the loan, then find the time period of the loan.

(10) What amount does Karen have to pay after 5 years if he takes a loan of $3950 at 3% simple interest?