Question

Suppose that you want to create a "college fund" for your newborn child and place $300 in a bank account at the end of each of the next 20 years. If that account earns an annual rate of return of 7%, how much will be in that account at the end of the twentieth year?

Answer 1

Answer:

Amount at the end of twentieth year is $12,300

Explanation:

Annuity means a set of fixed amount of payments either made to you or paid by you , at a fixed number of times over a course of defined period.

The case given in the question is of ordinary annuity , where fixed amount of payment are required at the end of each period.

FORMULA FOR FUTURE VALUE ORDINARY ANNUITY =

               

Where, C(cash flow) = $300,

            I(interest rate) = 7%

           N(number of period) = 20

           FV ( Future value)

$FUTURE\ VALUE(FV)\ OF\ ORDINARY\ ANNUITY= CASH\ FLOW(C)\times \left [ \frac{1+I^{N}-1}{I} \right ])$

$FUTURE\ VALUE(FV)\ OF\ ORDINARY\ ANNUITY= \ 300\times \left [ \frac{1+7\%^{20}-1}{7\%} \right ])$

$FUTURE\ VALUE(FV)\ OF\ ORDINARY\ ANNUITY= \ 300\times \left [ \frac{\ 1.07\ ^{20}-1}{7\%} \right ])$

$FUTURE\ VALUE(FV)\ OF\ ORDINARY\ ANNUITY= \ 300\times \left [ \frac{\ 3.87\ -1}{7\%} \right ])$

$FUTURE\ VALUE(FV)\ OF\ ORDINARY\ ANNUITY= \ 300\times \left [ \frac{\ 2.87}{7\%} \right ])$

= 861/7%

= $12,300