Simple Interest
Math MCQs

Question :    How much loan did Kimberly borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8312.5 to clear it?

Correct Answer  $6650

Solution & Explanation

Solution

Given,

Amount (A) = $8312.5

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

$8312.5 = P (1 + 5% × 5)

⇒ $8312.5 = P (1 + ⁵/₁₀₀ × 5)

⇒ $8312.5 = P (1 + ^{5 × 5}/₁₀₀)

⇒ $8312.5 = P (1 + ²⁵/₁₀₀)

⇒ $8312.5 = P (^{100 + 25}/₁₀₀)

⇒ $8312.5 = P × ¹²⁵/₁₀₀

⇒ P × ¹²⁵/₁₀₀ = $8312.5

⇒ P = ^8312.5/_¹²⁵/100

⇒ P = 8312.5 × ¹⁰⁰/₁₂₅

⇒ P = ^{8312.5 × 100}/₁₂₅

⇒ P = ⁸³¹²⁵⁰/₁₂₅

⇒ P = $6650

Thus, the sum borrowed (P) = $6650 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 8312.5, then the Principal = ¹⁰⁰/₁₂₅ × 8312.5

= ^{100 × 8312.5}/₁₂₅

= ⁸³¹²⁵⁰/₁₂₅

= 6650

Thus, Principal = $6650

Thus, the sum borrowed = $6650 Answer

Similar Questions

(1) What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 8% simple interest?

(2) Jennifer had to pay $3542.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(3) What amount does Linda have to pay after 6 years if he takes a loan of $3350 at 6% simple interest?

(4) Michelle had to pay $5544 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(5) Calculate the amount due if Patricia borrowed a sum of $3150 at 8% simple interest for 3 years.

(6) Lisa took a loan of $6100 at the rate of 7% simple interest per annum. If he paid an amount of $9943 to clear the loan, then find the time period of the loan.

(7) Patricia took a loan of $4300 at the rate of 7% simple interest per annum. If he paid an amount of $7310 to clear the loan, then find the time period of the loan.

(8) Calculate the amount due after 10 years if Barbara borrowed a sum of $5550 at a rate of 7% simple interest.

(9) What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 8% simple interest?

(10) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 6% simple interest?