Simple Interest
Math MCQs

Question :    Michael took a loan of $4600 at the rate of 8% simple interest per annum. If he paid an amount of $8280 to clear the loan, then find the time period of the loan.

Correct Answer  10

Solution & Explanation

Solution

Given,

Principal (P) = $4600

Rate of Simple Interest (R) = 8% per annum

Amount (A) = $8280

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 = $8280 – $4600 = $3680

Thus, Simple Interest = $3680

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 × 3680}/_{4600 × 8}

= ³⁶⁸⁰⁰⁰/₃₆₈₀₀

= 10 years (using formula)

Thus, Time (T) = 10 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) = $4600

Rate of Simple Interest (R) = 8% per annum

Simple Interest = $3680 (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 = 8% of Principal

= 8% of $4600

= ⁸/₁₀₀ × 4600

= ^{8 × 4600}/₁₀₀

= ³⁶⁸⁰⁰/₁₀₀ = 368

Thus, simple Interest for 1 year = $368

Now,

∵ If the simple Interest is $368, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₃₆₈ years

∴ If the simple Interest is $3680, then the time = ¹/₃₆₈ × 3680 years

= ^{1 × 3680}/₃₆₈ years

= ³⁶⁸⁰/₃₆₈ = 10 years

Thus, time (T) = 10 years Answer

Similar Questions

(1) How much loan did Sandra borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7095 to clear it?

(2) How much loan did Daniel borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7015 to clear it?

(3) Calculate the amount due if Jessica borrowed a sum of $3750 at 3% simple interest for 3 years.

(4) Calculate the amount due if Sarah borrowed a sum of $3850 at 4% simple interest for 4 years.

(5) Find the amount to be paid if Joseph borrowed a sum of $5700 at 2% simple interest for 7 years.

(6) If James borrowed $3000 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.

(7) Calculate the amount due after 9 years if Michael borrowed a sum of $5300 at a rate of 3% simple interest.

(8) What amount does Michael have to pay after 5 years if he takes a loan of $3300 at 3% simple interest?

(9) If Sandra paid $4984 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(10) Jennifer took a loan of $4500 at the rate of 10% simple interest per annum. If he paid an amount of $9000 to clear the loan, then find the time period of the loan.