Simple Interest
Math MCQs

Question :    How much loan did Sharon borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9687.5 to clear it?

Correct Answer  $7750

Solution & Explanation

Solution

Given,

Amount (A) = $9687.5

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

$9687.5 = P (1 + 5% × 5)

⇒ $9687.5 = P (1 + ⁵/₁₀₀ × 5)

⇒ $9687.5 = P (1 + ^{5 × 5}/₁₀₀)

⇒ $9687.5 = P (1 + ²⁵/₁₀₀)

⇒ $9687.5 = P (^{100 + 25}/₁₀₀)

⇒ $9687.5 = P × ¹²⁵/₁₀₀

⇒ P × ¹²⁵/₁₀₀ = $9687.5

⇒ P = ^9687.5/_¹²⁵/100

⇒ P = 9687.5 × ¹⁰⁰/₁₂₅

⇒ P = ^{9687.5 × 100}/₁₂₅

⇒ P = ⁹⁶⁸⁷⁵⁰/₁₂₅

⇒ P = $7750

Thus, the sum borrowed (P) = $7750 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 9687.5, then the Principal = ¹⁰⁰/₁₂₅ × 9687.5

= ^{100 × 9687.5}/₁₂₅

= ⁹⁶⁸⁷⁵⁰/₁₂₅

= 7750

Thus, Principal = $7750

Thus, the sum borrowed = $7750 Answer

Similar Questions

(1) What amount does Mary have to pay after 5 years if he takes a loan of $3050 at 8% simple interest?

(2) What amount does Karen have to pay after 6 years if he takes a loan of $3950 at 9% simple interest?

(3) Calculate the amount due if Christopher borrowed a sum of $4000 at 4% simple interest for 4 years.

(4) In how much time a principal of $3150 will amount to $3780 at a simple interest of 5% per annum?

(5) How much loan did Mark borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7040 to clear it?

(6) Find the amount to be paid if Mary borrowed a sum of $5050 at 3% simple interest for 7 years.

(7) David took a loan of $4800 at the rate of 9% simple interest per annum. If he paid an amount of $9120 to clear the loan, then find the time period of the loan.

(8) What amount will be due after 2 years if Matthew borrowed a sum of $3600 at a 6% simple interest?

(9) Linda took a loan of $4700 at the rate of 6% simple interest per annum. If he paid an amount of $6392 to clear the loan, then find the time period of the loan.

(10) Find the amount to be paid if John borrowed a sum of $5200 at 7% simple interest for 7 years.