Simple Interest
Math MCQs

Question :    Anthony took a loan of $6600 at the rate of 6% simple interest per annum. If he paid an amount of $10164 to clear the loan, then find the time period of the loan.

Correct Answer  9

Solution & Explanation

Solution

Given,

Principal (P) = $6600

Rate of Simple Interest (R) = 6% per annum

Amount (A) = $10164

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 = $10164 – $6600 = $3564

Thus, Simple Interest = $3564

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 × 3564}/_{6600 × 6}

= ³⁵⁶⁴⁰⁰/₃₉₆₀₀

= 9 years (using formula)

Thus, Time (T) = 9 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) = $6600

Rate of Simple Interest (R) = 6% per annum

Simple Interest = $3564 (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 = 6% of Principal

= 6% of $6600

= ⁶/₁₀₀ × 6600

= ^{6 × 6600}/₁₀₀

= ³⁹⁶⁰⁰/₁₀₀ = 396

Thus, simple Interest for 1 year = $396

Now,

∵ If the simple Interest is $396, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₃₉₆ years

∴ If the simple Interest is $3564, then the time = ¹/₃₉₆ × 3564 years

= ^{1 × 3564}/₃₉₆ years

= ³⁵⁶⁴/₃₉₆ = 9 years

Thus, time (T) = 9 years Answer

Similar Questions

(1) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 3% simple interest?

(2) Robert took a loan of $4200 at the rate of 8% simple interest per annum. If he paid an amount of $6216 to clear the loan, then find the time period of the loan.

(3) Find the amount to be paid if Michael borrowed a sum of $5300 at 7% simple interest for 7 years.

(4) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 3% simple interest?

(5) Find the amount to be paid if Barbara borrowed a sum of $5550 at 6% simple interest for 8 years.

(6) Calculate the amount due if Linda borrowed a sum of $3350 at 2% simple interest for 3 years.

(7) If Linda borrowed $3350 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.

(8) Calculate the amount due if Michael borrowed a sum of $3300 at 4% simple interest for 4 years.

(9) Find the amount to be paid if Jessica borrowed a sum of $5750 at 6% simple interest for 8 years.

(10) Mary took a loan of $4100 at the rate of 6% simple interest per annum. If he paid an amount of $6068 to clear the loan, then find the time period of the loan.