Simple Interest
Math MCQs

Question :    How much loan did Linda borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5885 to clear it?

Correct Answer  $5350

Solution & Explanation

Solution

Given,

Amount (A) = $5885

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

$5885 = P (1 + 2% × 5)

⇒ $5885 = P (1 + ²/₁₀₀ × 5)

⇒ $5885 = P (1 + ^{2 × 5}/₁₀₀)

⇒ $5885 = P (1 + ¹⁰/₁₀₀)

⇒ $5885 = P (^{100 + 10}/₁₀₀)

⇒ $5885 = P × ¹¹⁰/₁₀₀

⇒ P × ¹¹⁰/₁₀₀ = $5885

⇒ P = ⁵⁸⁸⁵/_¹¹⁰/100

⇒ P = 5885 × ¹⁰⁰/₁₁₀

⇒ P = ^{5885 × 100}/₁₁₀

⇒ P = ⁵⁸⁸⁵⁰⁰/₁₁₀

⇒ P = $5350

Thus, the sum borrowed (P) = $5350 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 5885, then the Principal = ¹⁰⁰/₁₁₀ × 5885

= ^{100 × 5885}/₁₁₀

= ⁵⁸⁸⁵⁰⁰/₁₁₀

= 5350

Thus, Principal = $5350

Thus, the sum borrowed = $5350 Answer

Similar Questions

(1) Joseph took a loan of $5400 at the rate of 10% simple interest per annum. If he paid an amount of $10260 to clear the loan, then find the time period of the loan.

(2) What amount does Karen have to pay after 5 years if he takes a loan of $3950 at 9% simple interest?

(3) Lisa had to pay $4293 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(4) What amount does Patricia have to pay after 5 years if he takes a loan of $3150 at 2% simple interest?

(5) If Charles borrowed $3900 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.

(6) Find the amount to be paid if Linda borrowed a sum of $5350 at 10% simple interest for 8 years.

(7) What amount does David have to pay after 5 years if he takes a loan of $3400 at 10% simple interest?

(8) What amount will be due after 2 years if James borrowed a sum of $3000 at a 9% simple interest?

(9) Christopher took a loan of $6000 at the rate of 9% simple interest per annum. If he paid an amount of $11400 to clear the loan, then find the time period of the loan.

(10) Calculate the amount due after 9 years if Charles borrowed a sum of $5900 at a rate of 7% simple interest.