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 5% simple interest?

(2) Patricia took a loan of $4300 at the rate of 10% simple interest per annum. If he paid an amount of $8170 to clear the loan, then find the time period of the loan.

(3) Calculate the amount due after 9 years if Robert borrowed a sum of $5100 at a rate of 10% simple interest.

(4) Calculate the amount due after 10 years if Mary borrowed a sum of $5050 at a rate of 3% simple interest.

(5) Find the amount to be paid if Richard borrowed a sum of $5600 at 3% simple interest for 7 years.

(6) If Lisa paid $4860 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(7) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 3% simple interest?

(8) What amount does John have to pay after 5 years if he takes a loan of $3200 at 5% simple interest?

(9) Find the amount to be paid if Thomas borrowed a sum of $5800 at 2% simple interest for 7 years.

(10) Anthony took a loan of $6600 at the rate of 6% simple interest per annum. If he paid an amount of $9372 to clear the loan, then find the time period of the loan.