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) Richard took a loan of $5200 at the rate of 6% simple interest per annum. If he paid an amount of $7072 to clear the loan, then find the time period of the loan.

(2) 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?

(3) Elizabeth took a loan of $4900 at the rate of 8% simple interest per annum. If he paid an amount of $8036 to clear the loan, then find the time period of the loan.

(4) What amount will be due after 2 years if James borrowed a sum of $3000 at a 10% simple interest?

(5) How much loan did George borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8760 to clear it?

(6) Calculate the amount due after 10 years if Michael borrowed a sum of $5300 at a rate of 2% simple interest.

(7) What amount will be due after 2 years if Steven borrowed a sum of $3800 at a 10% simple interest?

(8) Calculate the amount due after 10 years if Jessica borrowed a sum of $5750 at a rate of 6% simple interest.

(9) Calculate the amount due after 9 years if Linda borrowed a sum of $5350 at a rate of 5% simple interest.

(10) Calculate the amount due after 10 years if Richard borrowed a sum of $5600 at a rate of 2% simple interest.