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) Thomas had to pay $4028 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(2) What amount does James have to pay after 5 years if he takes a loan of $3000 at 2% simple interest?

(3) Richard took a loan of $5200 at the rate of 10% simple interest per annum. If he paid an amount of $10400 to clear the loan, then find the time period of the loan.

(4) In how much time a principal of $3050 will amount to $3355 at a simple interest of 2% per annum?

(5) Lisa took a loan of $6100 at the rate of 8% simple interest per annum. If he paid an amount of $10004 to clear the loan, then find the time period of the loan.

(6) Find the amount to be paid if James borrowed a sum of $5000 at 9% simple interest for 7 years.

(7) Sandra took a loan of $6900 at the rate of 10% simple interest per annum. If he paid an amount of $12420 to clear the loan, then find the time period of the loan.

(8) John took a loan of $4400 at the rate of 7% simple interest per annum. If he paid an amount of $6248 to clear the loan, then find the time period of the loan.

(9) How much loan did Laura borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $9027.5 to clear it?

(10) Calculate the amount due if David borrowed a sum of $3400 at 8% simple interest for 3 years.