Simple Interest
Math MCQs

Question :    How much loan did Sandra borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7417.5 to clear it?

Correct Answer  $6450

Solution & Explanation

Solution

Given,

Amount (A) = $7417.5

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

$7417.5 = P (1 + 3% × 5)

⇒ $7417.5 = P (1 + ³/₁₀₀ × 5)

⇒ $7417.5 = P (1 + ^{3 × 5}/₁₀₀)

⇒ $7417.5 = P (1 + ¹⁵/₁₀₀)

⇒ $7417.5 = P (^{100 + 15}/₁₀₀)

⇒ $7417.5 = P × ¹¹⁵/₁₀₀

⇒ P × ¹¹⁵/₁₀₀ = $7417.5

⇒ P = ^7417.5/_¹¹⁵/100

⇒ P = 7417.5 × ¹⁰⁰/₁₁₅

⇒ P = ^{7417.5 × 100}/₁₁₅

⇒ P = ⁷⁴¹⁷⁵⁰/₁₁₅

⇒ P = $6450

Thus, the sum borrowed (P) = $6450 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 7417.5, then the Principal = ¹⁰⁰/₁₁₅ × 7417.5

= ^{100 × 7417.5}/₁₁₅

= ⁷⁴¹⁷⁵⁰/₁₁₅

= 6450

Thus, Principal = $6450

Thus, the sum borrowed = $6450 Answer

Similar Questions

(1) Calculate the amount due if Christopher borrowed a sum of $4000 at 9% simple interest for 4 years.

(2) Find the amount to be paid if Mary borrowed a sum of $5050 at 5% simple interest for 8 years.

(3) How much loan did Cynthia borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9540 to clear it?

(4) Daniel took a loan of $6200 at the rate of 10% simple interest per annum. If he paid an amount of $11160 to clear the loan, then find the time period of the loan.

(5) What amount will be due after 2 years if Matthew borrowed a sum of $3600 at a 6% simple interest?

(6) John took a loan of $4400 at the rate of 10% simple interest per annum. If he paid an amount of $7040 to clear the loan, then find the time period of the loan.

(7) What amount does Patricia have to pay after 5 years if he takes a loan of $3150 at 4% simple interest?

(8) Patricia took a loan of $4300 at the rate of 6% simple interest per annum. If he paid an amount of $6106 to clear the loan, then find the time period of the loan.

(9) Calculate the amount due after 10 years if Barbara borrowed a sum of $5550 at a rate of 8% simple interest.

(10) What amount will be due after 2 years if Kenneth borrowed a sum of $4000 at a 6% simple interest?