Simple Interest
Math MCQs

Question :    Elizabeth took a loan of $4900 at the rate of 8% simple interest per annum. If he paid an amount of $8036 to clear the loan, then find the time period of the loan.

Correct Answer  8

Solution & Explanation

Solution

Given,

Principal (P) = $4900

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

Amount (A) = $8036

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 = $8036 – $4900 = $3136

Thus, Simple Interest = $3136

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 × 3136}/_{4900 × 8}

= ³¹³⁶⁰⁰/₃₉₂₀₀

= 8 years (using formula)

Thus, Time (T) = 8 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) = $4900

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

Simple Interest = $3136 (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 $4900

= ⁸/₁₀₀ × 4900

= ^{8 × 4900}/₁₀₀

= ³⁹²⁰⁰/₁₀₀ = 392

Thus, simple Interest for 1 year = $392

Now,

∵ If the simple Interest is $392, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₃₉₂ years

∴ If the simple Interest is $3136, then the time = ¹/₃₉₂ × 3136 years

= ^{1 × 3136}/₃₉₂ years

= ³¹³⁶/₃₉₂ = 8 years

Thus, time (T) = 8 years Answer

Similar Questions

(1) Calculate the amount due if Susan borrowed a sum of $3650 at 2% simple interest for 4 years.

(2) How much loan did Ashley borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7205 to clear it?

(3) Calculate the amount due if Christopher borrowed a sum of $4000 at 4% simple interest for 3 years.

(4) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 6% simple interest?

(5) Find the amount to be paid if Barbara borrowed a sum of $5550 at 9% simple interest for 7 years.

(6) Calculate the amount due after 9 years if Elizabeth borrowed a sum of $5450 at a rate of 3% simple interest.

(7) What amount will be due after 2 years if Paul borrowed a sum of $3850 at a 8% simple interest?

(8) If Daniel paid $4592 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(9) Michael took a loan of $4600 at the rate of 10% simple interest per annum. If he paid an amount of $8280 to clear the loan, then find the time period of the loan.

(10) Calculate the amount due after 9 years if Jessica borrowed a sum of $5750 at a rate of 2% simple interest.