Simple Interest
Math MCQs

Question :    Lisa took a loan of $6100 at the rate of 6% simple interest per annum. If he paid an amount of $9760 to clear the loan, then find the time period of the loan.

Correct Answer  10

Solution & Explanation

Solution

Given,

Principal (P) = $6100

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

Amount (A) = $9760

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 = $9760 – $6100 = $3660

Thus, Simple Interest = $3660

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 × 3660}/_{6100 × 6}

= ³⁶⁶⁰⁰⁰/₃₆₆₀₀

= 10 years (using formula)

Thus, Time (T) = 10 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) = 6% per annum

Simple Interest = $3660 (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 $6100

= ⁶/₁₀₀ × 6100

= ^{6 × 6100}/₁₀₀

= ³⁶⁶⁰⁰/₁₀₀ = 366

Thus, simple Interest for 1 year = $366

Now,

∵ If the simple Interest is $366, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₃₆₆ years

∴ If the simple Interest is $3660, then the time = ¹/₃₆₆ × 3660 years

= ^{1 × 3660}/₃₆₆ years

= ³⁶⁶⁰/₃₆₆ = 10 years

Thus, time (T) = 10 years Answer

Similar Questions

(1) Patricia took a loan of $4300 at the rate of 7% simple interest per annum. If he paid an amount of $7310 to clear the loan, then find the time period of the loan.

(2) How much loan did Cynthia borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9937.5 to clear it?

(3) Calculate the amount due if Christopher borrowed a sum of $4000 at 2% simple interest for 4 years.

(4) Karen had to pay $4424 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(5) Calculate the amount due after 10 years if Richard borrowed a sum of $5600 at a rate of 9% simple interest.

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

(7) In how much time a principal of $3050 will amount to $3233 at a simple interest of 2% per annum?

(8) Daniel had to pay $4346 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(9) Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 5% simple interest.

(10) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 3% simple interest?