Simple Interest
Math MCQs

Question :    How much loan did David borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6210 to clear it?

Correct Answer  $5400

Solution & Explanation

Solution

Given,

Amount (A) = $6210

Rate of Simple Interest (R) = 3%

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

$6210 = P (1 + 3% × 5)

⇒ $6210 = P (1 + ³/₁₀₀ × 5)

⇒ $6210 = P (1 + ^{3 × 5}/₁₀₀)

⇒ $6210 = P (1 + ¹⁵/₁₀₀)

⇒ $6210 = P (^{100 + 15}/₁₀₀)

⇒ $6210 = P × ¹¹⁵/₁₀₀

⇒ P × ¹¹⁵/₁₀₀ = $6210

⇒ P = ⁶²¹⁰/_¹¹⁵/100

⇒ P = 6210 × ¹⁰⁰/₁₁₅

⇒ P = ^{6210 × 100}/₁₁₅

⇒ P = ⁶²¹⁰⁰⁰/₁₁₅

⇒ P = $5400

Thus, the sum borrowed (P) = $5400 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 = 3% per annum

Thus, Interest = 3% of principal

⇒ Interest = 3% of 100 = 3

Thus, Simple Interest for 1 year = 3

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 × 3 = 15

Thus, simple interest for 5 years = 15

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 15 = 115

Calculation of the Principal

Now,

∵ If the Amount is 115, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₁₅

∴ If the Amount is 6210, then the Principal = ¹⁰⁰/₁₁₅ × 6210

= ^{100 × 6210}/₁₁₅

= ⁶²¹⁰⁰⁰/₁₁₅

= 5400

Thus, Principal = $5400

Thus, the sum borrowed = $5400 Answer

Similar Questions

(1) What amount does William have to pay after 6 years if he takes a loan of $3500 at 9% simple interest?

(2) What amount will be due after 2 years if Mark borrowed a sum of $3700 at a 7% simple interest?

(3) Calculate the amount due if Robert borrowed a sum of $3100 at 8% simple interest for 4 years.

(4) Daniel took a loan of $6200 at the rate of 8% simple interest per annum. If he paid an amount of $9176 to clear the loan, then find the time period of the loan.

(5) Nancy took a loan of $6300 at the rate of 6% simple interest per annum. If he paid an amount of $10080 to clear the loan, then find the time period of the loan.

(6) In how much time a principal of $3100 will amount to $3379 at a simple interest of 3% per annum?

(7) Find the amount to be paid if William borrowed a sum of $5500 at 10% simple interest for 7 years.

(8) John took a loan of $4400 at the rate of 7% simple interest per annum. If he paid an amount of $7480 to clear the loan, then find the time period of the loan.

(9) Calculate the amount due if Michael borrowed a sum of $3300 at 5% simple interest for 4 years.

(10) Thomas had to pay $4028 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.