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

(2) John took a loan of $4400 at the rate of 8% simple interest per annum. If he paid an amount of $7216 to clear the loan, then find the time period of the loan.

(3) What amount does Joseph have to pay after 5 years if he takes a loan of $3700 at 3% simple interest?

(4) Find the amount to be paid if William borrowed a sum of $5500 at 8% simple interest for 8 years.

(5) Thomas took a loan of $5600 at the rate of 9% simple interest per annum. If he paid an amount of $10640 to clear the loan, then find the time period of the loan.

(6) Calculate the amount due if James borrowed a sum of $3000 at 9% simple interest for 4 years.

(7) Linda took a loan of $4700 at the rate of 9% simple interest per annum. If he paid an amount of $8507 to clear the loan, then find the time period of the loan.

(8) What amount does Elizabeth have to pay after 6 years if he takes a loan of $3450 at 9% simple interest?

(9) Linda had to pay $3651.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(10) Calculate the amount due if Jennifer borrowed a sum of $3250 at 5% simple interest for 3 years.