Simple Interest
Math MCQs

Question :    William had to pay $3815 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  $3500

Solution & Explanation

Solution

Given,

Amount (A) = $3815

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

$3815 = P (1 + 3% × 3)

⇒ $3815 = P (1 + ³/₁₀₀ × 3)

⇒ $3815 = P (1 + ^{3 × 3}/₁₀₀)

⇒ $3815 = P (1 + ⁹/₁₀₀)

⇒ $3815 = P (^{100 + 9}/₁₀₀)

⇒ $3815 = P × ¹⁰⁹/₁₀₀

⇒ P × ¹⁰⁹/₁₀₀ = $3815

⇒ P = ³⁸¹⁵/_¹⁰⁹/100

⇒ P = 3815 × ¹⁰⁰/₁₀₉

⇒ P = ^{3815 × 100}/₁₀₉

⇒ P = ³⁸¹⁵⁰⁰/₁₀₉

⇒ P = $3500

Thus, the sum borrowed (P) = $3500 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 3815, then the Principal = ¹⁰⁰/₁₀₉ × 3815

= ^{100 × 3815}/₁₀₉

= ³⁸¹⁵⁰⁰/₁₀₉

= 3500

Thus, Principal = $3500

Thus, the sum borrowed = $3500 Answer

Similar Questions

(1) Andrew had to pay $5088 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

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

(3) What amount will be due after 2 years if William borrowed a sum of $3250 at a 10% simple interest?

(4) What amount does Jennifer have to pay after 6 years if he takes a loan of $3250 at 3% simple interest?

(5) How much loan did Susan borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7062.5 to clear it?

(6) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 9% simple interest for 8 years.

(7) What amount does David have to pay after 6 years if he takes a loan of $3400 at 7% simple interest?

(8) Richard took a loan of $5200 at the rate of 7% simple interest per annum. If he paid an amount of $8476 to clear the loan, then find the time period of the loan.

(9) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 7% simple interest?

(10) Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 5% simple interest.