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) Anthony took a loan of $6600 at the rate of 10% simple interest per annum. If he paid an amount of $13200 to clear the loan, then find the time period of the loan.

(2) Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 5% simple interest.

(3) Find the amount to be paid if Susan borrowed a sum of $5650 at 8% simple interest for 7 years.

(4) What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 6% simple interest?

(5) Jennifer took a loan of $4500 at the rate of 8% simple interest per annum. If he paid an amount of $8100 to clear the loan, then find the time period of the loan.

(6) Find the amount to be paid if Karen borrowed a sum of $5950 at 6% simple interest for 7 years.

(7) Christopher took a loan of $6000 at the rate of 8% simple interest per annum. If he paid an amount of $9840 to clear the loan, then find the time period of the loan.

(8) Find the amount to be paid if Sarah borrowed a sum of $5850 at 2% simple interest for 8 years.

(9) 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.

(10) Find the amount to be paid if Thomas borrowed a sum of $5800 at 3% simple interest for 8 years.