Simple Interest
Math MCQs

Question :    Joseph had to pay $4255 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

Correct Answer  $3700

Solution & Explanation

Solution

Given,

Amount (A) = $4255

Rate of Simple Interest (R) = 5%

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

$4255 = P (1 + 5% × 3)

⇒ $4255 = P (1 + ⁵/₁₀₀ × 3)

⇒ $4255 = P (1 + ^{5 × 3}/₁₀₀)

⇒ $4255 = P (1 + ¹⁵/₁₀₀)

⇒ $4255 = P (^{100 + 15}/₁₀₀)

⇒ $4255 = P × ¹¹⁵/₁₀₀

⇒ P × ¹¹⁵/₁₀₀ = $4255

⇒ P = ⁴²⁵⁵/_¹¹⁵/100

⇒ P = 4255 × ¹⁰⁰/₁₁₅

⇒ P = ^{4255 × 100}/₁₁₅

⇒ P = ⁴²⁵⁵⁰⁰/₁₁₅

⇒ P = $3700

Thus, the sum borrowed (P) = $3700 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 = 5% per annum

Thus, Interest = 5% of principal

⇒ Interest = 5% of 100 = 5

Thus, Simple Interest for 1 year = 5

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 × 5 = 15

Thus, simple interest for 3 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 4255, then the Principal = ¹⁰⁰/₁₁₅ × 4255

= ^{100 × 4255}/₁₁₅

= ⁴²⁵⁵⁰⁰/₁₁₅

= 3700

Thus, Principal = $3700

Thus, the sum borrowed = $3700 Answer

Similar Questions

(1) Daniel took a loan of $6200 at the rate of 8% simple interest per annum. If he paid an amount of $9672 to clear the loan, then find the time period of the loan.

(2) How much loan did Linda borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5885 to clear it?

(3) 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.

(4) Christopher took a loan of $6000 at the rate of 9% simple interest per annum. If he paid an amount of $11400 to clear the loan, then find the time period of the loan.

(5) How much loan did Dorothy borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8700 to clear it?

(6) Calculate the amount due after 10 years if Susan borrowed a sum of $5650 at a rate of 8% simple interest.

(7) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 10% simple interest?

(8) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 10% simple interest?

(9) Calculate the amount due if Mary borrowed a sum of $3050 at 4% simple interest for 3 years.

(10) Thomas had to pay $4028 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.