Simple Interest
Math MCQs

Question :    Betty took a loan of $6500 at the rate of 6% simple interest per annum. If he paid an amount of $9230 to clear the loan, then find the time period of the loan.

Correct Answer  7

Solution & Explanation

Solution

Given,

Principal (P) = $6500

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

Amount (A) = $9230

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 = $9230 – $6500 = $2730

Thus, Simple Interest = $2730

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 × 2730}/_{6500 × 6}

= ²⁷³⁰⁰⁰/₃₉₀₀₀

= 7 years (using formula)

Thus, Time (T) = 7 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) = $6500

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

Simple Interest = $2730 (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 $6500

= ⁶/₁₀₀ × 6500

= ^{6 × 6500}/₁₀₀

= ³⁹⁰⁰⁰/₁₀₀ = 390

Thus, simple Interest for 1 year = $390

Now,

∵ If the simple Interest is $390, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₃₉₀ years

∴ If the simple Interest is $2730, then the time = ¹/₃₉₀ × 2730 years

= ^{1 × 2730}/₃₉₀ years

= ²⁷³⁰/₃₉₀ = 7 years

Thus, time (T) = 7 years Answer

Similar Questions

(1) Richard had to pay $3924 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(2) What amount does James have to pay after 5 years if he takes a loan of $3000 at 6% simple interest?

(3) Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 9% simple interest.

(4) Linda took a loan of $4700 at the rate of 10% simple interest per annum. If he paid an amount of $8460 to clear the loan, then find the time period of the loan.

(5) If John paid $3712 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(6) Find the amount to be paid if Mary borrowed a sum of $5050 at 10% simple interest for 7 years.

(7) In how much time a principal of $3150 will amount to $3433.5 at a simple interest of 3% per annum?

(8) Lisa took a loan of $6100 at the rate of 8% simple interest per annum. If he paid an amount of $10004 to clear the loan, then find the time period of the loan.

(9) Karen took a loan of $5900 at the rate of 6% simple interest per annum. If he paid an amount of $9086 to clear the loan, then find the time period of the loan.

(10) Patricia had to pay $3433.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.