Simple Interest
Math MCQs

Question :    Anthony had to pay $4687 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

Correct Answer  $4300

Solution & Explanation

Solution

Given,

Amount (A) = $4687

Rate of Simple Interest (R) = 3%

Time (T) = 3 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

$4687 = P (1 + 3% × 3)

⇒ $4687 = P (1 + ³/₁₀₀ × 3)

⇒ $4687 = P (1 + ^{3 × 3}/₁₀₀)

⇒ $4687 = P (1 + ⁹/₁₀₀)

⇒ $4687 = P (^{100 + 9}/₁₀₀)

⇒ $4687 = P × ¹⁰⁹/₁₀₀

⇒ P × ¹⁰⁹/₁₀₀ = $4687

⇒ P = ⁴⁶⁸⁷/_¹⁰⁹/100

⇒ P = 4687 × ¹⁰⁰/₁₀₉

⇒ P = ^{4687 × 100}/₁₀₉

⇒ P = ⁴⁶⁸⁷⁰⁰/₁₀₉

⇒ P = $4300

Thus, the sum borrowed (P) = $4300 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 = 3 years

So, we need to calculate the simple interest for the given time period, which is 3 years

Thus, Simple Interest for 3 years = 3 × Simple Interest for 1 year

= 3 × 3 = 9

Thus, simple interest for 3 years = 9

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 9 = 109

Calculation of the Principal

Now,

∵ If the Amount is 109, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₀₉

∴ If the Amount is 4687, then the Principal = ¹⁰⁰/₁₀₉ × 4687

= ^{100 × 4687}/₁₀₉

= ⁴⁶⁸⁷⁰⁰/₁₀₉

= 4300

Thus, Principal = $4300

Thus, the sum borrowed = $4300 Answer

Similar Questions

(1) Find the amount to be paid if David borrowed a sum of $5400 at 6% simple interest for 7 years.

(2) Find the amount to be paid if Susan borrowed a sum of $5650 at 5% simple interest for 8 years.

(3) Find the amount to be paid if Karen borrowed a sum of $5950 at 6% simple interest for 8 years.

(4) What amount will be due after 2 years if Mark borrowed a sum of $3700 at a 6% simple interest?

(5) What amount does Michael have to pay after 5 years if he takes a loan of $3300 at 6% simple interest?

(6) How much loan did Andrew borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8500 to clear it?

(7) How much loan did Susan borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6497.5 to clear it?

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

(9) Mary took a loan of $4100 at the rate of 10% simple interest per annum. If he paid an amount of $6560 to clear the loan, then find the time period of the loan.

(10) Calculate the amount due if David borrowed a sum of $3400 at 6% simple interest for 4 years.