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Simple Interest
Math MCQs


Question :    Sarah took a loan of $5700 at the rate of 7% simple interest per annum. If he paid an amount of $8094 to clear the loan, then find the time period of the loan.


Correct Answer  6

Solution & Explanation

Solution

Given,

Principal (P) = $5700

Rate of Simple Interest (R) = 7% per annum

Amount (A) = $8094

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 = $8094 – $5700 = $2394

Thus, Simple Interest = $2394

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 × 2394/5700 × 7

= 239400/39900

= 6 years (using formula)

Thus, Time (T) = 6 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) = $5700

Rate of Simple Interest (R) = 7% per annum

Simple Interest = $2394 (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 = 7% of Principal

= 7% of $5700

= 7/100 × 5700

= 7 × 5700/100

= 39900/100 = 399

Thus, simple Interest for 1 year = $399

Now,

∵ If the simple Interest is $399, then the time = 1 year

∴ If the simple Interest is $1, then the time = 1/399 years

∴ If the simple Interest is $2394, then the time = 1/399 × 2394 years

= 1 × 2394/399 years

= 2394/399 = 6 years

Thus, time (T) = 6 years Answer


Similar Questions

(1) Calculate the amount due if Sarah borrowed a sum of $3850 at 9% simple interest for 3 years.

(2) What amount does Thomas have to pay after 5 years if he takes a loan of $3800 at 8% simple interest?

(3) What amount will be due after 2 years if Matthew borrowed a sum of $3600 at a 5% simple interest?

(4) How much loan did Michelle borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7992.5 to clear it?

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

(6) Margaret took a loan of $6700 at the rate of 8% simple interest per annum. If he paid an amount of $10452 to clear the loan, then find the time period of the loan.

(7) Find the amount to be paid if John borrowed a sum of $5200 at 8% simple interest for 8 years.

(8) In how much time a principal of $3000 will amount to $3600 at a simple interest of 4% per annum?

(9) Charles had to pay $4134 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(10) Find the amount to be paid if Christopher borrowed a sum of $6000 at 7% simple interest for 7 years.