Simple Interest
Math MCQs

Question :    Patricia took a loan of $4300 at the rate of 9% simple interest per annum. If he paid an amount of $7009 to clear the loan, then find the time period of the loan.

Correct Answer  7

Solution & Explanation

Solution

Given,

Principal (P) = $4300

Rate of Simple Interest (R) = 9% per annum

Amount (A) = $7009

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 = $7009 – $4300 = $2709

Thus, Simple Interest = $2709

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 × 2709}/_{4300 × 9}

= ²⁷⁰⁹⁰⁰/₃₈₇₀₀

= 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) = $4300

Rate of Simple Interest (R) = 9% per annum

Simple Interest = $2709 (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 = 9% of Principal

= 9% of $4300

= ⁹/₁₀₀ × 4300

= ^{9 × 4300}/₁₀₀

= ³⁸⁷⁰⁰/₁₀₀ = 387

Thus, simple Interest for 1 year = $387

Now,

∵ If the simple Interest is $387, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₃₈₇ years

∴ If the simple Interest is $2709, then the time = ¹/₃₈₇ × 2709 years

= ^{1 × 2709}/₃₈₇ years

= ²⁷⁰⁹/₃₈₇ = 7 years

Thus, time (T) = 7 years Answer

Similar Questions

(1) How much loan did Mary borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6312.5 to clear it?

(2) How much loan did Sharon borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9687.5 to clear it?

(3) Sandra had to pay $4984 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(4) Elizabeth took a loan of $4900 at the rate of 8% simple interest per annum. If he paid an amount of $8820 to clear the loan, then find the time period of the loan.

(5) In how much time a principal of $3050 will amount to $3660 at a simple interest of 4% per annum?

(6) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 4% simple interest?

(7) Charles took a loan of $5800 at the rate of 10% simple interest per annum. If he paid an amount of $9280 to clear the loan, then find the time period of the loan.

(8) Betty took a loan of $6500 at the rate of 10% simple interest per annum. If he paid an amount of $10400 to clear the loan, then find the time period of the loan.

(9) What amount will be due after 2 years if Joshua borrowed a sum of $3950 at a 10% simple interest?

(10) Matthew took a loan of $6400 at the rate of 10% simple interest per annum. If he paid an amount of $12800 to clear the loan, then find the time period of the loan.