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) William took a loan of $5000 at the rate of 9% simple interest per annum. If he paid an amount of $8600 to clear the loan, then find the time period of the loan.

(2) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 3% simple interest?

(3) In how much time a principal of $3150 will amount to $3654 at a simple interest of 4% per annum?

(4) Calculate the amount due if Joseph borrowed a sum of $3700 at 2% simple interest for 3 years.

(5) David took a loan of $4800 at the rate of 9% simple interest per annum. If he paid an amount of $8688 to clear the loan, then find the time period of the loan.

(6) Anthony took a loan of $6600 at the rate of 10% simple interest per annum. If he paid an amount of $12540 to clear the loan, then find the time period of the loan.

(7) How much loan did James borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $5750 to clear it?

(8) If Jennifer borrowed $3250 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.

(9) What amount will be due after 2 years if Paul borrowed a sum of $3850 at a 7% simple interest?

(10) Calculate the amount due after 9 years if Susan borrowed a sum of $5650 at a rate of 5% simple interest.