Simple Interest
Math MCQs

Question :    Mary took a loan of $4100 at the rate of 8% simple interest per annum. If he paid an amount of $6068 to clear the loan, then find the time period of the loan.

Correct Answer  6

Solution & Explanation

Solution

Given,

Principal (P) = $4100

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

Amount (A) = $6068

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 = $6068 – $4100 = $1968

Thus, Simple Interest = $1968

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 × 1968}/_{4100 × 8}

= ¹⁹⁶⁸⁰⁰/₃₂₈₀₀

= 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) = $4100

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

Simple Interest = $1968 (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 $4100

= ⁸/₁₀₀ × 4100

= ^{8 × 4100}/₁₀₀

= ³²⁸⁰⁰/₁₀₀ = 328

Thus, simple Interest for 1 year = $328

Now,

∵ If the simple Interest is $328, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₃₂₈ years

∴ If the simple Interest is $1968, then the time = ¹/₃₂₈ × 1968 years

= ^{1 × 1968}/₃₂₈ years

= ¹⁹⁶⁸/₃₂₈ = 6 years

Thus, time (T) = 6 years Answer

Similar Questions

(1) Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 8% simple interest.

(2) Calculate the amount due after 9 years if Charles borrowed a sum of $5900 at a rate of 3% simple interest.

(3) How much loan did Richard borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6440 to clear it?

(4) Thomas took a loan of $5600 at the rate of 8% simple interest per annum. If he paid an amount of $8288 to clear the loan, then find the time period of the loan.

(5) How much loan did Mark borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7360 to clear it?

(6) Betty took a loan of $6500 at the rate of 7% simple interest per annum. If he paid an amount of $9230 to clear the loan, then find the time period of the loan.

(7) Calculate the amount due after 9 years if Thomas borrowed a sum of $5800 at a rate of 10% simple interest.

(8) 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?

(9) In how much time a principal of $3050 will amount to $3294 at a simple interest of 4% per annum?

(10) 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.