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 will be due after 2 years if John borrowed a sum of $3100 at a 8% simple interest?

(2) How much loan did Patricia borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6437.5 to clear it?

(3) Jennifer took a loan of $4500 at the rate of 7% simple interest per annum. If he paid an amount of $6705 to clear the loan, then find the time period of the loan.

(4) What amount will be due after 2 years if Mark borrowed a sum of $3700 at a 4% simple interest?

(5) Jessica had to pay $4200 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(6) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 3% simple interest?

(7) If Ashley paid $5460 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(8) Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 7% simple interest.

(9) How much loan did David borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6480 to clear it?

(10) Michael took a loan of $4600 at the rate of 10% simple interest per annum. If he paid an amount of $7820 to clear the loan, then find the time period of the loan.