Simple Interest
Math MCQs

Question :    Jessica took a loan of $5500 at the rate of 10% simple interest per annum. If he paid an amount of $8800 to clear the loan, then find the time period of the loan.

Correct Answer  6

Solution & Explanation

Solution

Given,

Principal (P) = $5500

Rate of Simple Interest (R) = 10% per annum

Amount (A) = $8800

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 = $8800 – $5500 = $3300

Thus, Simple Interest = $3300

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 × 3300}/_{5500 × 10}

= ³³⁰⁰⁰⁰/₅₅₀₀₀

= 6 years (using formula)

Thus, Time (T) = 6 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) = $5500

Rate of Simple Interest (R) = 10% per annum

Simple Interest = $3300 (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 = 10% of Principal

= 10% of $5500

= ¹⁰/₁₀₀ × 5500

= ^{10 × 5500}/₁₀₀

= ⁵⁵⁰⁰⁰/₁₀₀ = 550

Thus, simple Interest for 1 year = $550

Now,

∵ If the simple Interest is $550, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₅₅₀ years

∴ If the simple Interest is $3300, then the time = ¹/₅₅₀ × 3300 years

= ^{1 × 3300}/₅₅₀ years

= ³³⁰⁰/₅₅₀ = 6 years

Thus, time (T) = 6 years Answer

Similar Questions

(1) Patricia took a loan of $4300 at the rate of 7% simple interest per annum. If he paid an amount of $7009 to clear the loan, then find the time period of the loan.

(2) Robert took a loan of $4200 at the rate of 8% simple interest per annum. If he paid an amount of $7224 to clear the loan, then find the time period of the loan.

(3) Find the amount to be paid if Barbara borrowed a sum of $5550 at 2% simple interest for 7 years.

(4) Christopher took a loan of $6000 at the rate of 7% simple interest per annum. If he paid an amount of $10200 to clear the loan, then find the time period of the loan.

(5) Barbara had to pay $4082.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(6) Anthony took a loan of $6600 at the rate of 9% simple interest per annum. If he paid an amount of $10758 to clear the loan, then find the time period of the loan.

(7) How much loan did Ronald borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8250 to clear it?

(8) Donald took a loan of $7000 at the rate of 9% simple interest per annum. If he paid an amount of $12040 to clear the loan, then find the time period of the loan.

(9) Calculate the amount due if William borrowed a sum of $3500 at 8% simple interest for 3 years.

(10) Find the amount to be paid if Barbara borrowed a sum of $5550 at 4% simple interest for 7 years.