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) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 9% simple interest?

(2) Elizabeth took a loan of $4900 at the rate of 8% simple interest per annum. If he paid an amount of $8428 to clear the loan, then find the time period of the loan.

(3) Calculate the amount due after 9 years if Charles borrowed a sum of $5900 at a rate of 5% simple interest.

(4) If James paid $3360 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(5) Calculate the amount due if Michael borrowed a sum of $3300 at 6% simple interest for 4 years.

(6) Mary had to pay $3416 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(7) Barbara took a loan of $5100 at the rate of 8% simple interest per annum. If he paid an amount of $7548 to clear the loan, then find the time period of the loan.

(8) How much loan did Margaret borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7620 to clear it?

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

(10) Find the amount to be paid if Susan borrowed a sum of $5650 at 6% simple interest for 7 years.