Simple Interest
Math MCQs

Question :    William took a loan of $5000 at the rate of 7% simple interest per annum. If he paid an amount of $8150 to clear the loan, then find the time period of the loan.

Correct Answer  9

Solution & Explanation

Solution

Given,

Principal (P) = $5000

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

Amount (A) = $8150

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 = $8150 – $5000 = $3150

Thus, Simple Interest = $3150

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 × 3150}/_{5000 × 7}

= ³¹⁵⁰⁰⁰/₃₅₀₀₀

= 9 years (using formula)

Thus, Time (T) = 9 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) = $5000

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

Simple Interest = $3150 (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 $5000

= ⁷/₁₀₀ × 5000

= ^{7 × 5000}/₁₀₀

= ³⁵⁰⁰⁰/₁₀₀ = 350

Thus, simple Interest for 1 year = $350

Now,

∵ If the simple Interest is $350, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₃₅₀ years

∴ If the simple Interest is $3150, then the time = ¹/₃₅₀ × 3150 years

= ^{1 × 3150}/₃₅₀ years

= ³¹⁵⁰/₃₅₀ = 9 years

Thus, time (T) = 9 years Answer

Similar Questions

(1) Calculate the amount due if Michael borrowed a sum of $3300 at 9% simple interest for 4 years.

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

(3) How much loan did John borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $5980 to clear it?

(4) Linda took a loan of $4700 at the rate of 7% simple interest per annum. If he paid an amount of $7003 to clear the loan, then find the time period of the loan.

(5) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 2% simple interest?

(6) What amount does Barbara have to pay after 5 years if he takes a loan of $3550 at 8% simple interest?

(7) Nancy took a loan of $6300 at the rate of 6% simple interest per annum. If he paid an amount of $9702 to clear the loan, then find the time period of the loan.

(8) Find the amount to be paid if Sarah borrowed a sum of $5850 at 4% simple interest for 7 years.

(9) Calculate the amount due if Robert borrowed a sum of $3100 at 7% simple interest for 4 years.

(10) Elizabeth took a loan of $4900 at the rate of 6% simple interest per annum. If he paid an amount of $7840 to clear the loan, then find the time period of the loan.