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) What amount does John have to pay after 5 years if he takes a loan of $3200 at 7% simple interest?

(2) What amount does William have to pay after 6 years if he takes a loan of $3500 at 4% simple interest?

(3) Find the amount to be paid if William borrowed a sum of $5500 at 9% simple interest for 8 years.

(4) Betty took a loan of $6500 at the rate of 8% simple interest per annum. If he paid an amount of $11700 to clear the loan, then find the time period of the loan.

(5) Susan took a loan of $5300 at the rate of 6% simple interest per annum. If he paid an amount of $7208 to clear the loan, then find the time period of the loan.

(6) What amount does Thomas have to pay after 5 years if he takes a loan of $3800 at 4% simple interest?

(7) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 3% simple interest?

(8) Calculate the amount due after 10 years if John borrowed a sum of $5200 at a rate of 9% simple interest.

(9) Find the amount to be paid if Jessica borrowed a sum of $5750 at 6% simple interest for 7 years.

(10) In how much time a principal of $3150 will amount to $3528 at a simple interest of 4% per annum?