Simple Interest
Math MCQs

Question :    How much loan did Michael borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6625 to clear it?

Correct Answer  $5300

Solution & Explanation

Solution

Given,

Amount (A) = $6625

Rate of Simple Interest (R) = 5%

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

$6625 = P (1 + 5% × 5)

⇒ $6625 = P (1 + ⁵/₁₀₀ × 5)

⇒ $6625 = P (1 + ^{5 × 5}/₁₀₀)

⇒ $6625 = P (1 + ²⁵/₁₀₀)

⇒ $6625 = P (^{100 + 25}/₁₀₀)

⇒ $6625 = P × ¹²⁵/₁₀₀

⇒ P × ¹²⁵/₁₀₀ = $6625

⇒ P = ⁶⁶²⁵/_¹²⁵/100

⇒ P = 6625 × ¹⁰⁰/₁₂₅

⇒ P = ^{6625 × 100}/₁₂₅

⇒ P = ⁶⁶²⁵⁰⁰/₁₂₅

⇒ P = $5300

Thus, the sum borrowed (P) = $5300 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 = 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 × 5 = 25

Thus, simple interest for 5 years = 25

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 25 = 125

Calculation of the Principal

Now,

∵ If the Amount is 125, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₂₅

∴ If the Amount is 6625, then the Principal = ¹⁰⁰/₁₂₅ × 6625

= ^{100 × 6625}/₁₂₅

= ⁶⁶²⁵⁰⁰/₁₂₅

= 5300

Thus, Principal = $5300

Thus, the sum borrowed = $5300 Answer

Similar Questions

(1) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 2% simple interest for 4 years.

(2) Calculate the amount due after 10 years if Jennifer borrowed a sum of $5250 at a rate of 2% simple interest.

(3) Calculate the amount due if Mary borrowed a sum of $3050 at 10% simple interest for 3 years.

(4) Find the amount to be paid if Mary borrowed a sum of $5050 at 8% simple interest for 7 years.

(5) Calculate the amount due if Joseph borrowed a sum of $3700 at 4% simple interest for 3 years.

(6) Calculate the amount due if Michael borrowed a sum of $3300 at 4% simple interest for 3 years.

(7) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 3% simple interest for 7 years.

(8) If Susan borrowed $3650 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.

(9) Robert took a loan of $4200 at the rate of 10% simple interest per annum. If he paid an amount of $7140 to clear the loan, then find the time period of the loan.

(10) David had to pay $3706 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.