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) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 8% simple interest?

(2) Find the amount to be paid if Linda borrowed a sum of $5350 at 6% simple interest for 8 years.

(3) Find the amount to be paid if Michael borrowed a sum of $5300 at 3% simple interest for 7 years.

(4) If Michael paid $3828 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 if Mary borrowed a sum of $3050 at 9% simple interest for 4 years.

(6) If Susan borrowed $3650 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.

(7) James took a loan of $4000 at the rate of 6% simple interest per annum. If he paid an amount of $5680 to clear the loan, then find the time period of the loan.

(8) How much loan did Barbara borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6105 to clear it?

(9) Find the amount to be paid if Susan borrowed a sum of $5650 at 6% simple interest for 7 years.

(10) Betty took a loan of $6500 at the rate of 9% simple interest per annum. If he paid an amount of $10595 to clear the loan, then find the time period of the loan.