Simple Interest
Math MCQs

Question :    How much loan did Richard borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6160 to clear it?

Correct Answer  $5600

Solution & Explanation

Solution

Given,

Amount (A) = $6160

Rate of Simple Interest (R) = 2%

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

$6160 = P (1 + 2% × 5)

⇒ $6160 = P (1 + ²/₁₀₀ × 5)

⇒ $6160 = P (1 + ^{2 × 5}/₁₀₀)

⇒ $6160 = P (1 + ¹⁰/₁₀₀)

⇒ $6160 = P (^{100 + 10}/₁₀₀)

⇒ $6160 = P × ¹¹⁰/₁₀₀

⇒ P × ¹¹⁰/₁₀₀ = $6160

⇒ P = ⁶¹⁶⁰/_¹¹⁰/100

⇒ P = 6160 × ¹⁰⁰/₁₁₀

⇒ P = ^{6160 × 100}/₁₁₀

⇒ P = ⁶¹⁶⁰⁰⁰/₁₁₀

⇒ P = $5600

Thus, the sum borrowed (P) = $5600 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 = 2% per annum

Thus, Interest = 2% of principal

⇒ Interest = 2% of 100 = 2

Thus, Simple Interest for 1 year = 2

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 × 2 = 10

Thus, simple interest for 5 years = 10

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 10 = 110

Calculation of the Principal

Now,

∵ If the Amount is 110, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₁₀

∴ If the Amount is 6160, then the Principal = ¹⁰⁰/₁₁₀ × 6160

= ^{100 × 6160}/₁₁₀

= ⁶¹⁶⁰⁰⁰/₁₁₀

= 5600

Thus, Principal = $5600

Thus, the sum borrowed = $5600 Answer

Similar Questions

(1) Christopher had to pay $4600 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(2) If Emily paid $5700 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(3) Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 7% simple interest.

(4) John had to pay $3392 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(5) Find the amount to be paid if Barbara borrowed a sum of $5550 at 10% simple interest for 8 years.

(6) If James paid $3360 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(7) Mark took a loan of $6800 at the rate of 9% simple interest per annum. If he paid an amount of $10472 to clear the loan, then find the time period of the loan.

(8) How much loan did Richard borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7000 to clear it?

(9) Find the amount to be paid if Joseph borrowed a sum of $5700 at 2% simple interest for 8 years.

(10) What amount will be due after 2 years if William borrowed a sum of $3250 at a 7% simple interest?