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) Calculate the amount due after 9 years if Jennifer borrowed a sum of $5250 at a rate of 2% simple interest.

(2) Jennifer had to pay $3640 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(3) Calculate the amount due after 10 years if Jessica borrowed a sum of $5750 at a rate of 5% simple interest.

(4) Donald took a loan of $7000 at the rate of 10% simple interest per annum. If he paid an amount of $11900 to clear the loan, then find the time period of the loan.

(5) Robert took a loan of $4200 at the rate of 10% simple interest per annum. If he paid an amount of $7980 to clear the loan, then find the time period of the loan.

(6) Joseph took a loan of $5400 at the rate of 6% simple interest per annum. If he paid an amount of $7992 to clear the loan, then find the time period of the loan.

(7) Nancy took a loan of $6300 at the rate of 6% simple interest per annum. If he paid an amount of $8946 to clear the loan, then find the time period of the loan.

(8) Calculate the amount due after 10 years if Mary borrowed a sum of $5050 at a rate of 4% simple interest.

(9) Calculate the amount due after 10 years if Robert borrowed a sum of $5100 at a rate of 4% simple interest.

(10) How much loan did Michael borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6625 to clear it?