Simple Interest
Math MCQs

Question :    Lisa took a loan of $6100 at the rate of 9% simple interest per annum. If he paid an amount of $10492 to clear the loan, then find the time period of the loan.

Correct Answer  8

Solution & Explanation

Solution

Given,

Principal (P) = $6100

Rate of Simple Interest (R) = 9% per annum

Amount (A) = $10492

Thus, time (T) = ?

Method (1) Using Formula

Calculation of Simple Interest, when Principal and Amount are given

Formual to Calculate Simple Interest when Principal and Amount are given

We know that, Amount (A) = Principal (P) + Simple Interest (SI)

⇒ Simple Interest (SI) = Amount – Principal

⇒ SI = $10492 – $6100 = $4392

Thus, Simple Interest = $4392

Calculation of the Time using forumula when Amount, Simple Interest and Principal are known

Formula to find the Time (T)

Time (T) = ^{100 × Simple Interest}/_{Principal × Rate of Interest}

⇒ T = ^{100 × SI}/_{P × R}

Thus, Time (T) = ^{100 × 4392}/_{6100 × 9}

= ⁴³⁹²⁰⁰/₅₄₉₀₀

= 8 years (using formula)

Thus, Time (T) = 8 years (from time taken before calculation)Answer

Calculation of the Time using Unitary Method when Amount, Simple Interest and Principal are known

Here, we have

Principal (P) = $6100

Rate of Simple Interest (R) = 9% per annum

Simple Interest = $4392 (As calculated above by subtracting Principal from the Amount given)

We know that, interest is calculated on the basis of the Principal.

This means Simple Interest for 1 year = Rate of simple interest × Principal

Thus, Simple Interest for 1 year = 9% of Principal

= 9% of $6100

= ⁹/₁₀₀ × 6100

= ^{9 × 6100}/₁₀₀

= ⁵⁴⁹⁰⁰/₁₀₀ = 549

Thus, simple Interest for 1 year = $549

Now,

∵ If the simple Interest is $549, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₅₄₉ years

∴ If the simple Interest is $4392, then the time = ¹/₅₄₉ × 4392 years

= ^{1 × 4392}/₅₄₉ years

= ⁴³⁹²/₅₄₉ = 8 years

Thus, time (T) = 8 years Answer

Similar Questions

(1) Robert took a loan of $4200 at the rate of 10% simple interest per annum. If he paid an amount of $8400 to clear the loan, then find the time period of the loan.

(2) Calculate the amount due after 10 years if Elizabeth borrowed a sum of $5450 at a rate of 7% simple interest.

(3) Calculate the amount due if James borrowed a sum of $3000 at 2% simple interest for 3 years.

(4) Calculate the amount due after 9 years if Christopher borrowed a sum of $6000 at a rate of 2% simple interest.

(5) Donald took a loan of $7000 at the rate of 9% simple interest per annum. If he paid an amount of $13300 to clear the loan, then find the time period of the loan.

(6) How much loan did Daniel borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7320 to clear it?

(7) Linda took a loan of $4700 at the rate of 10% simple interest per annum. If he paid an amount of $8460 to clear the loan, then find the time period of the loan.

(8) Sandra had to pay $4850.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(9) Find the amount to be paid if Susan borrowed a sum of $5650 at 8% simple interest for 8 years.

(10) Calculate the amount due if David borrowed a sum of $3400 at 4% simple interest for 3 years.