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Simple Interest
Math MCQs


Question :    Patricia took a loan of $4300 at the rate of 6% simple interest per annum. If he paid an amount of $5848 to clear the loan, then find the time period of the loan.


Correct Answer  6

Solution & Explanation

Solution

Given,

Principal (P) = $4300

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

Amount (A) = $5848

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 = $5848 – $4300 = $1548

Thus, Simple Interest = $1548

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 × 1548/4300 × 6

= 154800/25800

= 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) = $4300

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

Simple Interest = $1548 (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 $4300

= 6/100 × 4300

= 6 × 4300/100

= 25800/100 = 258

Thus, simple Interest for 1 year = $258

Now,

∵ If the simple Interest is $258, then the time = 1 year

∴ If the simple Interest is $1, then the time = 1/258 years

∴ If the simple Interest is $1548, then the time = 1/258 × 1548 years

= 1 × 1548/258 years

= 1548/258 = 6 years

Thus, time (T) = 6 years Answer


Similar Questions

(1) What amount does Patricia have to pay after 5 years if he takes a loan of $3150 at 8% simple interest?

(2) Find the amount to be paid if Robert borrowed a sum of $5100 at 7% simple interest for 8 years.

(3) Matthew took a loan of $6400 at the rate of 7% simple interest per annum. If he paid an amount of $10880 to clear the loan, then find the time period of the loan.

(4) How much loan did Ryan borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8690 to clear it?

(5) Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 2% simple interest.

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

(7) Karen took a loan of $5900 at the rate of 7% simple interest per annum. If he paid an amount of $8378 to clear the loan, then find the time period of the loan.

(8) Susan took a loan of $5300 at the rate of 6% simple interest per annum. If he paid an amount of $8162 to clear the loan, then find the time period of the loan.

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

(10) Linda had to pay $3651.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.