Simple Interest
Math MCQs

Question :    Lisa took a loan of $6100 at the rate of 10% simple interest per annum. If he paid an amount of $10980 to clear the loan, then find the time period of the loan.

Correct Answer  8

Solution & Explanation

Solution

Given,

Principal (P) = $6100

Rate of Simple Interest (R) = 10% per annum

Amount (A) = $10980

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 = $10980 – $6100 = $4880

Thus, Simple Interest = $4880

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 × 4880}/_{6100 × 10}

= ⁴⁸⁸⁰⁰⁰/₆₁₀₀₀

= 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) = $6100

Rate of Simple Interest (R) = 10% per annum

Simple Interest = $4880 (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 = 10% of Principal

= 10% of $6100

= ¹⁰/₁₀₀ × 6100

= ^{10 × 6100}/₁₀₀

= ⁶¹⁰⁰⁰/₁₀₀ = 610

Thus, simple Interest for 1 year = $610

Now,

∵ If the simple Interest is $610, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₆₁₀ years

∴ If the simple Interest is $4880, then the time = ¹/₆₁₀ × 4880 years

= ^{1 × 4880}/₆₁₀ years

= ⁴⁸⁸⁰/₆₁₀ = 8 years

Thus, time (T) = 8 years Answer

Similar Questions

(1) In how much time a principal of $3100 will amount to $3348 at a simple interest of 4% per annum?

(2) Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 10% simple interest.

(3) Calculate the amount due if Sarah borrowed a sum of $3850 at 3% simple interest for 4 years.

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

(5) How much loan did Daniel borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7625 to clear it?

(6) David had to pay $3910 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(7) Margaret took a loan of $6700 at the rate of 10% simple interest per annum. If he paid an amount of $12730 to clear the loan, then find the time period of the loan.

(8) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 3% simple interest?

(9) Find the amount to be paid if Patricia borrowed a sum of $5150 at 6% simple interest for 7 years.

(10) David had to pay $3604 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.