Simple Interest
Math MCQs

Question :    Sandra took a loan of $6900 at the rate of 10% simple interest per annum. If he paid an amount of $13110 to clear the loan, then find the time period of the loan.

Correct Answer  9

Solution & Explanation

Solution

Given,

Principal (P) = $6900

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

Amount (A) = $13110

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 = $13110 – $6900 = $6210

Thus, Simple Interest = $6210

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 × 6210}/_{6900 × 10}

= ⁶²¹⁰⁰⁰/₆₉₀₀₀

= 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) = $6900

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

Simple Interest = $6210 (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 $6900

= ¹⁰/₁₀₀ × 6900

= ^{10 × 6900}/₁₀₀

= ⁶⁹⁰⁰⁰/₁₀₀ = 690

Thus, simple Interest for 1 year = $690

Now,

∵ If the simple Interest is $690, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₆₉₀ years

∴ If the simple Interest is $6210, then the time = ¹/₆₉₀ × 6210 years

= ^{1 × 6210}/₆₉₀ years

= ⁶²¹⁰/₆₉₀ = 9 years

Thus, time (T) = 9 years Answer

Similar Questions

(1) Sarah had to pay $4312 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(2) Calculate the amount due if Susan borrowed a sum of $3650 at 9% simple interest for 3 years.

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

(4) Calculate the amount due if Linda borrowed a sum of $3350 at 10% simple interest for 4 years.

(5) If Michael paid $3696 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(6) If Mary paid $3538 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(7) Kenneth had to pay $5750 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(8) What amount will be due after 2 years if William borrowed a sum of $3250 at a 4% simple interest?

(9) What amount does Richard have to pay after 6 years if he takes a loan of $3600 at 8% simple interest?

(10) Find the amount to be paid if Jessica borrowed a sum of $5750 at 5% simple interest for 7 years.