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 $8976 to clear the loan, then find the time period of the loan.

Correct Answer  6

Solution & Explanation

Solution

Given,

Principal (P) = $6600

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

Amount (A) = $8976

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 = $8976 – $6600 = $2376

Thus, Simple Interest = $2376

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 × 2376}/_{6600 × 6}

= ²³⁷⁶⁰⁰/₃₉₆₀₀

= 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) = $6600

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

Simple Interest = $2376 (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 $2376, then the time = ¹/₃₉₆ × 2376 years

= ^{1 × 2376}/₃₉₆ years

= ²³⁷⁶/₃₉₆ = 6 years

Thus, time (T) = 6 years Answer

Similar Questions

(1) What amount does Linda have to pay after 6 years if he takes a loan of $3350 at 8% simple interest?

(2) Find the amount to be paid if Patricia borrowed a sum of $5150 at 2% simple interest for 7 years.

(3) How much loan did Michael borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6360 to clear it?

(4) Calculate the amount due after 10 years if Susan borrowed a sum of $5650 at a rate of 2% simple interest.

(5) If James paid $3480 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(6) Charles took a loan of $5800 at the rate of 7% simple interest per annum. If he paid an amount of $9454 to clear the loan, then find the time period of the loan.

(7) Jessica took a loan of $5500 at the rate of 7% simple interest per annum. If he paid an amount of $8580 to clear the loan, then find the time period of the loan.

(8) Find the amount to be paid if Linda borrowed a sum of $5350 at 8% simple interest for 8 years.

(9) Sarah took a loan of $5700 at the rate of 8% simple interest per annum. If he paid an amount of $8892 to clear the loan, then find the time period of the loan.

(10) Calculate the amount due if Joseph borrowed a sum of $3700 at 5% simple interest for 4 years.