Simple Interest
Math MCQs

Question :    How much loan did Jason borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8855 to clear it?

Correct Answer  $7700

Solution & Explanation

Solution

Given,

Amount (A) = $8855

Rate of Simple Interest (R) = 3%

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

$8855 = P (1 + 3% × 5)

⇒ $8855 = P (1 + ³/₁₀₀ × 5)

⇒ $8855 = P (1 + ^{3 × 5}/₁₀₀)

⇒ $8855 = P (1 + ¹⁵/₁₀₀)

⇒ $8855 = P (^{100 + 15}/₁₀₀)

⇒ $8855 = P × ¹¹⁵/₁₀₀

⇒ P × ¹¹⁵/₁₀₀ = $8855

⇒ P = ⁸⁸⁵⁵/_¹¹⁵/100

⇒ P = 8855 × ¹⁰⁰/₁₁₅

⇒ P = ^{8855 × 100}/₁₁₅

⇒ P = ⁸⁸⁵⁵⁰⁰/₁₁₅

⇒ P = $7700

Thus, the sum borrowed (P) = $7700 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 = 3% per annum

Thus, Interest = 3% of principal

⇒ Interest = 3% of 100 = 3

Thus, Simple Interest for 1 year = 3

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 × 3 = 15

Thus, simple interest for 5 years = 15

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 15 = 115

Calculation of the Principal

Now,

∵ If the Amount is 115, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₁₅

∴ If the Amount is 8855, then the Principal = ¹⁰⁰/₁₁₅ × 8855

= ^{100 × 8855}/₁₁₅

= ⁸⁸⁵⁵⁰⁰/₁₁₅

= 7700

Thus, Principal = $7700

Thus, the sum borrowed = $7700 Answer

Similar Questions

(1) Calculate the amount due after 9 years if John borrowed a sum of $5200 at a rate of 8% simple interest.

(2) Lisa took a loan of $6100 at the rate of 10% simple interest per annum. If he paid an amount of $10370 to clear the loan, then find the time period of the loan.

(3) Donald took a loan of $7000 at the rate of 7% simple interest per annum. If he paid an amount of $11900 to clear the loan, then find the time period of the loan.

(4) Find the amount to be paid if Thomas borrowed a sum of $5800 at 7% simple interest for 8 years.

(5) In how much time a principal of $3100 will amount to $3565 at a simple interest of 3% per annum?

(6) What amount does Jessica have to pay after 6 years if he takes a loan of $3750 at 10% simple interest?

(7) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 7% simple interest?

(8) Margaret took a loan of $6700 at the rate of 8% simple interest per annum. If he paid an amount of $12060 to clear the loan, then find the time period of the loan.

(9) What amount does William have to pay after 6 years if he takes a loan of $3500 at 5% simple interest?

(10) How much loan did Deborah borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8567.5 to clear it?