Simple Interest
Math MCQs

Question :    How much loan did Andrew borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8500 to clear it?

Correct Answer  $6800

Solution & Explanation

Solution

Given,

Amount (A) = $8500

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

$8500 = P (1 + 5% × 5)

⇒ $8500 = P (1 + ⁵/₁₀₀ × 5)

⇒ $8500 = P (1 + ^{5 × 5}/₁₀₀)

⇒ $8500 = P (1 + ²⁵/₁₀₀)

⇒ $8500 = P (^{100 + 25}/₁₀₀)

⇒ $8500 = P × ¹²⁵/₁₀₀

⇒ P × ¹²⁵/₁₀₀ = $8500

⇒ P = ⁸⁵⁰⁰/_¹²⁵/100

⇒ P = 8500 × ¹⁰⁰/₁₂₅

⇒ P = ^{8500 × 100}/₁₂₅

⇒ P = ⁸⁵⁰⁰⁰⁰/₁₂₅

⇒ P = $6800

Thus, the sum borrowed (P) = $6800 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 8500, then the Principal = ¹⁰⁰/₁₂₅ × 8500

= ^{100 × 8500}/₁₂₅

= ⁸⁵⁰⁰⁰⁰/₁₂₅

= 6800

Thus, Principal = $6800

Thus, the sum borrowed = $6800 Answer

Similar Questions

(1) What amount will be due after 2 years if Michael borrowed a sum of $3150 at a 9% simple interest?

(2) Find the amount to be paid if David borrowed a sum of $5400 at 9% simple interest for 8 years.

(3) Donald took a loan of $7000 at the rate of 9% simple interest per annum. If he paid an amount of $10780 to clear the loan, then find the time period of the loan.

(4) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 2% simple interest for 8 years.

(5) What amount will be due after 2 years if Daniel borrowed a sum of $3550 at a 9% simple interest?

(6) Calculate the amount due if Karen borrowed a sum of $3950 at 5% simple interest for 3 years.

(7) Barbara took a loan of $5100 at the rate of 8% simple interest per annum. If he paid an amount of $7956 to clear the loan, then find the time period of the loan.

(8) David took a loan of $4800 at the rate of 10% simple interest per annum. If he paid an amount of $9120 to clear the loan, then find the time period of the loan.

(9) If Betty paid $4760 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(10) David took a loan of $4800 at the rate of 8% simple interest per annum. If he paid an amount of $7872 to clear the loan, then find the time period of the loan.