Simple Interest
Math MCQs

Question :    How much loan did Daniel borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7015 to clear it?

Correct Answer  $6100

Solution & Explanation

Solution

Given,

Amount (A) = $7015

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

$7015 = P (1 + 3% × 5)

⇒ $7015 = P (1 + ³/₁₀₀ × 5)

⇒ $7015 = P (1 + ^{3 × 5}/₁₀₀)

⇒ $7015 = P (1 + ¹⁵/₁₀₀)

⇒ $7015 = P (^{100 + 15}/₁₀₀)

⇒ $7015 = P × ¹¹⁵/₁₀₀

⇒ P × ¹¹⁵/₁₀₀ = $7015

⇒ P = ⁷⁰¹⁵/_¹¹⁵/100

⇒ P = 7015 × ¹⁰⁰/₁₁₅

⇒ P = ^{7015 × 100}/₁₁₅

⇒ P = ⁷⁰¹⁵⁰⁰/₁₁₅

⇒ P = $6100

Thus, the sum borrowed (P) = $6100 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 7015, then the Principal = ¹⁰⁰/₁₁₅ × 7015

= ^{100 × 7015}/₁₁₅

= ⁷⁰¹⁵⁰⁰/₁₁₅

= 6100

Thus, Principal = $6100

Thus, the sum borrowed = $6100 Answer

Similar Questions

(1) What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 10% simple interest?

(2) How much loan did Lisa borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7260 to clear it?

(3) Calculate the amount due if David borrowed a sum of $3400 at 6% simple interest for 3 years.

(4) In how much time a principal of $3100 will amount to $3596 at a simple interest of 4% per annum?

(5) How much loan did Rebecca borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8415 to clear it?

(6) Barbara had to pay $4082.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(7) John took a loan of $4400 at the rate of 7% simple interest per annum. If he paid an amount of $6556 to clear the loan, then find the time period of the loan.

(8) David took a loan of $4800 at the rate of 8% simple interest per annum. If he paid an amount of $8256 to clear the loan, then find the time period of the loan.

(9) Daniel took a loan of $6200 at the rate of 6% simple interest per annum. If he paid an amount of $9920 to clear the loan, then find the time period of the loan.

(10) Find the amount to be paid if William borrowed a sum of $5500 at 2% simple interest for 7 years.