Simple Interest
Math MCQs

Question :    Thomas took a loan of $5600 at the rate of 6% simple interest per annum. If he paid an amount of $8288 to clear the loan, then find the time period of the loan.

Correct Answer  8

Solution & Explanation

Solution

Given,

Principal (P) = $5600

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

Amount (A) = $8288

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 = $8288 – $5600 = $2688

Thus, Simple Interest = $2688

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 × 2688}/_{5600 × 6}

= ²⁶⁸⁸⁰⁰/₃₃₆₀₀

= 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) = $5600

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

Simple Interest = $2688 (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 $5600

= ⁶/₁₀₀ × 5600

= ^{6 × 5600}/₁₀₀

= ³³⁶⁰⁰/₁₀₀ = 336

Thus, simple Interest for 1 year = $336

Now,

∵ If the simple Interest is $336, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₃₃₆ years

∴ If the simple Interest is $2688, then the time = ¹/₃₃₆ × 2688 years

= ^{1 × 2688}/₃₃₆ years

= ²⁶⁸⁸/₃₃₆ = 8 years

Thus, time (T) = 8 years Answer

Similar Questions

(1) Elizabeth took a loan of $4900 at the rate of 8% simple interest per annum. If he paid an amount of $7644 to clear the loan, then find the time period of the loan.

(2) Calculate the amount due if William borrowed a sum of $3500 at 2% simple interest for 4 years.

(3) What amount does Barbara have to pay after 6 years if he takes a loan of $3550 at 7% simple interest?

(4) What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 2% simple interest?

(5) Richard took a loan of $5200 at the rate of 6% simple interest per annum. If he paid an amount of $8320 to clear the loan, then find the time period of the loan.

(6) Calculate the amount due if Christopher borrowed a sum of $4000 at 10% simple interest for 4 years.

(7) If Thomas borrowed $3800 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.

(8) Calculate the amount due after 9 years if Thomas borrowed a sum of $5800 at a rate of 3% simple interest.

(9) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 8% simple interest?

(10) Calculate the amount due after 10 years if Michael borrowed a sum of $5300 at a rate of 5% simple interest.