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) Jennifer had to pay $3542.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(2) Donald took a loan of $7000 at the rate of 7% simple interest per annum. If he paid an amount of $9940 to clear the loan, then find the time period of the loan.

(3) If Elizabeth borrowed $3450 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.

(4) What amount does Michael have to pay after 5 years if he takes a loan of $3300 at 4% simple interest?

(5) Margaret took a loan of $6700 at the rate of 8% simple interest per annum. If he paid an amount of $12060 to clear the loan, then find the time period of the loan.

(6) Joshua had to pay $5488 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(7) Calculate the amount due if Susan borrowed a sum of $3650 at 3% simple interest for 4 years.

(8) Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 10% simple interest.

(9) If Matthew paid $4872 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(10) Mary took a loan of $4100 at the rate of 6% simple interest per annum. If he paid an amount of $6314 to clear the loan, then find the time period of the loan.