Simple Interest
Math MCQs

Question :    Daniel took a loan of $6200 at the rate of 10% simple interest per annum. If he paid an amount of $9920 to clear the loan, then find the time period of the loan.

Correct Answer  6

Solution & Explanation

Solution

Given,

Principal (P) = $6200

Rate of Simple Interest (R) = 10% per annum

Amount (A) = $9920

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 = $9920 – $6200 = $3720

Thus, Simple Interest = $3720

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 × 3720}/_{6200 × 10}

= ³⁷²⁰⁰⁰/₆₂₀₀₀

= 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) = $6200

Rate of Simple Interest (R) = 10% per annum

Simple Interest = $3720 (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 = 10% of Principal

= 10% of $6200

= ¹⁰/₁₀₀ × 6200

= ^{10 × 6200}/₁₀₀

= ⁶²⁰⁰⁰/₁₀₀ = 620

Thus, simple Interest for 1 year = $620

Now,

∵ If the simple Interest is $620, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₆₂₀ years

∴ If the simple Interest is $3720, then the time = ¹/₆₂₀ × 3720 years

= ^{1 × 3720}/₆₂₀ years

= ³⁷²⁰/₆₂₀ = 6 years

Thus, time (T) = 6 years Answer

Similar Questions

(1) Find the amount to be paid if James borrowed a sum of $5000 at 8% simple interest for 7 years.

(2) What amount does James have to pay after 5 years if he takes a loan of $3000 at 7% simple interest?

(3) Calculate the amount due after 10 years if Susan borrowed a sum of $5650 at a rate of 9% simple interest.

(4) Calculate the amount due if Sarah borrowed a sum of $3850 at 2% simple interest for 3 years.

(5) What amount will be due after 2 years if Donald borrowed a sum of $3750 at a 4% simple interest?

(6) Elizabeth took a loan of $4900 at the rate of 7% simple interest per annum. If he paid an amount of $6958 to clear the loan, then find the time period of the loan.

(7) Calculate the amount due if Susan borrowed a sum of $3650 at 8% simple interest for 4 years.

(8) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 5% simple interest?

(9) In how much time a principal of $3000 will amount to $3450 at a simple interest of 3% per annum?

(10) What amount will be due after 2 years if William borrowed a sum of $3250 at a 9% simple interest?