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) Margaret had to pay $4611 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(2) Anthony took a loan of $6600 at the rate of 7% simple interest per annum. If he paid an amount of $9834 to clear the loan, then find the time period of the loan.

(3) Calculate the amount due after 9 years if Joseph borrowed a sum of $5700 at a rate of 5% simple interest.

(4) Calculate the amount due after 9 years if Susan borrowed a sum of $5650 at a rate of 10% simple interest.

(5) Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 3% simple interest.

(6) Barbara took a loan of $5100 at the rate of 9% simple interest per annum. If he paid an amount of $9690 to clear the loan, then find the time period of the loan.

(7) Daniel had to pay $4346 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(8) Robert took a loan of $4200 at the rate of 7% simple interest per annum. If he paid an amount of $6258 to clear the loan, then find the time period of the loan.

(9) Mary took a loan of $4100 at the rate of 7% simple interest per annum. If he paid an amount of $5822 to clear the loan, then find the time period of the loan.

(10) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 10% simple interest?