Simple Interest
Math MCQs

Question :    How much loan did Carol borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8107.5 to clear it?

Correct Answer  $7050

Solution & Explanation

Solution

Given,

Amount (A) = $8107.5

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

$8107.5 = P (1 + 3% × 5)

⇒ $8107.5 = P (1 + ³/₁₀₀ × 5)

⇒ $8107.5 = P (1 + ^{3 × 5}/₁₀₀)

⇒ $8107.5 = P (1 + ¹⁵/₁₀₀)

⇒ $8107.5 = P (^{100 + 15}/₁₀₀)

⇒ $8107.5 = P × ¹¹⁵/₁₀₀

⇒ P × ¹¹⁵/₁₀₀ = $8107.5

⇒ P = ^8107.5/_¹¹⁵/100

⇒ P = 8107.5 × ¹⁰⁰/₁₁₅

⇒ P = ^{8107.5 × 100}/₁₁₅

⇒ P = ⁸¹⁰⁷⁵⁰/₁₁₅

⇒ P = $7050

Thus, the sum borrowed (P) = $7050 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 8107.5, then the Principal = ¹⁰⁰/₁₁₅ × 8107.5

= ^{100 × 8107.5}/₁₁₅

= ⁸¹⁰⁷⁵⁰/₁₁₅

= 7050

Thus, Principal = $7050

Thus, the sum borrowed = $7050 Answer

Similar Questions

(1) Susan took a loan of $5300 at the rate of 7% simple interest per annum. If he paid an amount of $8268 to clear the loan, then find the time period of the loan.

(2) What amount does Richard have to pay after 6 years if he takes a loan of $3600 at 2% simple interest?

(3) What amount does James have to pay after 5 years if he takes a loan of $3000 at 5% simple interest?

(4) Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 6% simple interest.

(5) In how much time a principal of $3100 will amount to $3720 at a simple interest of 4% per annum?

(6) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 6% simple interest for 7 years.

(7) Calculate the amount due if James borrowed a sum of $3000 at 9% simple interest for 3 years.

(8) Find the amount to be paid if Christopher borrowed a sum of $6000 at 2% simple interest for 7 years.

(9) Jessica had to pay $4200 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(10) What amount does Joseph have to pay after 5 years if he takes a loan of $3700 at 8% simple interest?