Question

Allissa's employer offers its workers an optional two-month unpaid vacation after seven years of service to the firm. Alissa, who just started working for the firm plans to spend her vacation touring Asia at an estimated cost of $24000. To finance her trip, Alissa plans to make a deposit of $2500 into a savings account at the end of each of the next seven years ( the first deposit will occur one year from today). The account pays 8% annual interest. a) Will Alissa's account balance in seven years be enough to pay for her trip? b) Suppose Alissa increases her annual deposit to $2700. How large will her account be in seven years? Show your working using a calculator.

Answer 1

Estimated Cost of Asia vacation trip = $24000

a). Deposit made by alissa at the end of each of the next seven years = $ 2500

Annual Interest Rate = 8%

Since, 1st payment is made at the end of first year we will use Future Value(FV) of ordinary annuity formula:-

FV

where, C= annual Payment ;= $2500

i = interest rate ;= 8%

n= no. of payments = 7

FV

FV = $22307.0084

So, Alissa requires $ 24000 in 7 years to finance the trip but annual payments of $2500 will fetch her only $ 22307.0084 in 7 years. Hence, its not enough.

b). Deposit made by alissa at the end of each of the next seven years = $ 2700

Annual Interest Rate = 8%

Since, 1st payment is made at the end of first year we will use Future Value(FV) of ordinary annuity formula:-

FV

where, C= annual Payment ;= $2700

i = interest rate ;= 8%

n= no. of payments = 7

FV

FV = $24091.5691

So, Alissa requires $ 24000 in 7 years to finance the trip and the annual payments of $2700 will fetch her $ 24091.5691 in 7 years. Hence, its account will be large enough to finance the trip.

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