Simple Interest
Math MCQs

Question :    Lisa took a loan of $6100 at the rate of 8% simple interest per annum. If he paid an amount of $9516 to clear the loan, then find the time period of the loan.

Correct Answer  7

Solution & Explanation

Solution

Given,

Principal (P) = $6100

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

Amount (A) = $9516

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 = $9516 – $6100 = $3416

Thus, Simple Interest = $3416

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 × 3416}/_{6100 × 8}

= ³⁴¹⁶⁰⁰/₄₈₈₀₀

= 7 years (using formula)

Thus, Time (T) = 7 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) = $6100

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

Simple Interest = $3416 (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 $6100

= ⁸/₁₀₀ × 6100

= ^{8 × 6100}/₁₀₀

= ⁴⁸⁸⁰⁰/₁₀₀ = 488

Thus, simple Interest for 1 year = $488

Now,

∵ If the simple Interest is $488, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₈₈ years

∴ If the simple Interest is $3416, then the time = ¹/₄₈₈ × 3416 years

= ^{1 × 3416}/₄₈₈ years

= ³⁴¹⁶/₄₈₈ = 7 years

Thus, time (T) = 7 years Answer

Similar Questions

(1) What amount does Jessica have to pay after 6 years if he takes a loan of $3750 at 4% simple interest?

(2) How much loan did Jacob borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $9200 to clear it?

(3) How much loan did Barbara borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6105 to clear it?

(4) How much loan did Brian borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8280 to clear it?

(5) Calculate the amount due if Thomas borrowed a sum of $3800 at 3% simple interest for 4 years.

(6) Calculate the amount due if Richard borrowed a sum of $3600 at 10% simple interest for 4 years.

(7) What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 10% simple interest?

(8) What amount will be due after 2 years if Donald borrowed a sum of $3750 at a 9% simple interest?

(9) Margaret took a loan of $6700 at the rate of 10% simple interest per annum. If he paid an amount of $10720 to clear the loan, then find the time period of the loan.

(10) What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 10% simple interest?