Simple Interest
Math MCQs

Question :    Betty took a loan of $6500 at the rate of 10% simple interest per annum. If he paid an amount of $12350 to clear the loan, then find the time period of the loan.

Correct Answer  9

Solution & Explanation

Solution

Given,

Principal (P) = $6500

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

Amount (A) = $12350

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 = $12350 – $6500 = $5850

Thus, Simple Interest = $5850

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 × 5850}/_{6500 × 10}

= ⁵⁸⁵⁰⁰⁰/₆₅₀₀₀

= 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) = $6500

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

Simple Interest = $5850 (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 $6500

= ¹⁰/₁₀₀ × 6500

= ^{10 × 6500}/₁₀₀

= ⁶⁵⁰⁰⁰/₁₀₀ = 650

Thus, simple Interest for 1 year = $650

Now,

∵ If the simple Interest is $650, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₆₅₀ years

∴ If the simple Interest is $5850, then the time = ¹/₆₅₀ × 5850 years

= ^{1 × 5850}/₆₅₀ years

= ⁵⁸⁵⁰/₆₅₀ = 9 years

Thus, time (T) = 9 years Answer

Similar Questions

(1) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 10% simple interest?

(2) Kimberly had to pay $4929 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(3) David took a loan of $4800 at the rate of 9% simple interest per annum. If he paid an amount of $8688 to clear the loan, then find the time period of the loan.

(4) How much loan did Brian borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7920 to clear it?

(5) Elizabeth took a loan of $4900 at the rate of 9% simple interest per annum. If he paid an amount of $8869 to clear the loan, then find the time period of the loan.

(6) How much loan did Timothy borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9250 to clear it?

(7) Find the amount to be paid if Susan borrowed a sum of $5650 at 6% simple interest for 8 years.

(8) What amount will be due after 2 years if Steven borrowed a sum of $3800 at a 7% simple interest?

(9) Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 7% simple interest.

(10) William took a loan of $5000 at the rate of 9% simple interest per annum. If he paid an amount of $9050 to clear the loan, then find the time period of the loan.