Simple Interest
Math MCQs

Question :    Thomas took a loan of $5600 at the rate of 6% simple interest per annum. If he paid an amount of $8960 to clear the loan, then find the time period of the loan.

Correct Answer  10

Solution & Explanation

Solution

Given,

Principal (P) = $5600

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

Amount (A) = $8960

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 = $8960 – $5600 = $3360

Thus, Simple Interest = $3360

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 × 3360}/_{5600 × 6}

= ³³⁶⁰⁰⁰/₃₃₆₀₀

= 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) = $5600

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

Simple Interest = $3360 (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 $5600

= ⁶/₁₀₀ × 5600

= ^{6 × 5600}/₁₀₀

= ³³⁶⁰⁰/₁₀₀ = 336

Thus, simple Interest for 1 year = $336

Now,

∵ If the simple Interest is $336, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₃₃₆ years

∴ If the simple Interest is $3360, then the time = ¹/₃₃₆ × 3360 years

= ^{1 × 3360}/₃₃₆ years

= ³³⁶⁰/₃₃₆ = 10 years

Thus, time (T) = 10 years Answer

Similar Questions

(1) Jessica took a loan of $5500 at the rate of 6% simple interest per annum. If he paid an amount of $7480 to clear the loan, then find the time period of the loan.

(2) Find the amount to be paid if Michael borrowed a sum of $5300 at 7% simple interest for 7 years.

(3) What amount will be due after 2 years if Joseph borrowed a sum of $3350 at a 5% simple interest?

(4) Elizabeth took a loan of $4900 at the rate of 6% simple interest per annum. If he paid an amount of $6664 to clear the loan, then find the time period of the loan.

(5) Calculate the amount due if David borrowed a sum of $3400 at 5% simple interest for 3 years.

(6) William took a loan of $5000 at the rate of 8% simple interest per annum. If he paid an amount of $8600 to clear the loan, then find the time period of the loan.

(7) What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 3% simple interest?

(8) Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 6% simple interest.

(9) What amount will be due after 2 years if Michael borrowed a sum of $3150 at a 4% simple interest?

(10) David took a loan of $4800 at the rate of 10% simple interest per annum. If he paid an amount of $7680 to clear the loan, then find the time period of the loan.