Simple Interest
Math MCQs

Question :    How much loan did Kevin borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8875 to clear it?

Correct Answer  $7100

Solution & Explanation

Solution

Given,

Amount (A) = $8875

Rate of Simple Interest (R) = 5%

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

$8875 = P (1 + 5% × 5)

⇒ $8875 = P (1 + ⁵/₁₀₀ × 5)

⇒ $8875 = P (1 + ^{5 × 5}/₁₀₀)

⇒ $8875 = P (1 + ²⁵/₁₀₀)

⇒ $8875 = P (^{100 + 25}/₁₀₀)

⇒ $8875 = P × ¹²⁵/₁₀₀

⇒ P × ¹²⁵/₁₀₀ = $8875

⇒ P = ⁸⁸⁷⁵/_¹²⁵/100

⇒ P = 8875 × ¹⁰⁰/₁₂₅

⇒ P = ^{8875 × 100}/₁₂₅

⇒ P = ⁸⁸⁷⁵⁰⁰/₁₂₅

⇒ P = $7100

Thus, the sum borrowed (P) = $7100 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 = 5% per annum

Thus, Interest = 5% of principal

⇒ Interest = 5% of 100 = 5

Thus, Simple Interest for 1 year = 5

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 × 5 = 25

Thus, simple interest for 5 years = 25

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 25 = 125

Calculation of the Principal

Now,

∵ If the Amount is 125, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₂₅

∴ If the Amount is 8875, then the Principal = ¹⁰⁰/₁₂₅ × 8875

= ^{100 × 8875}/₁₂₅

= ⁸⁸⁷⁵⁰⁰/₁₂₅

= 7100

Thus, Principal = $7100

Thus, the sum borrowed = $7100 Answer

Similar Questions

(1) What amount will be due after 2 years if Anthony borrowed a sum of $3650 at a 8% simple interest?

(2) What amount will be due after 2 years if Thomas borrowed a sum of $3400 at a 5% simple interest?

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

(4) What amount does Barbara have to pay after 6 years if he takes a loan of $3550 at 4% simple interest?

(5) Find the amount to be paid if James borrowed a sum of $5000 at 3% simple interest for 7 years.

(6) Charles took a loan of $5800 at the rate of 6% simple interest per annum. If he paid an amount of $9280 to clear the loan, then find the time period of the loan.

(7) What amount does Linda have to pay after 5 years if he takes a loan of $3350 at 4% simple interest?

(8) Sarah had to pay $4427.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(9) Calculate the amount due if Thomas borrowed a sum of $3800 at 4% simple interest for 4 years.

(10) In how much time a principal of $3200 will amount to $3584 at a simple interest of 3% per annum?