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

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

Step-by-step 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)* \left [ (1+I^(N)-1)/(I) \right ])`

`FUTURE\ VALUE(FV)\ OF\ ORDINARY\ ANNUITY= \$300* \left [ (1+7\%^(20)-1)/(7\%) \right ])`

`FUTURE\ VALUE(FV)\ OF\ ORDINARY\ ANNUITY= \$300* \left [ (\ 1.07\ ^(20)-1)/(7\%) \right ])`

`FUTURE\ VALUE(FV)\ OF\ ORDINARY\ ANNUITY= \$300* \left [ (\ 3.87\ -1)/(7\%) \right ])`

`FUTURE\ VALUE(FV)\ OF\ ORDINARY\ ANNUITY= \$300* \left [ (\ 2.87)/(7\%) \right ])`

= 861/7%

= $12,300