1. Sharon wants to retire in 30 years time, and so decides to start a new retire
ID: 2382710 • Letter: 1
Question
1. Sharon wants to retire in 30 years time, and so decides to start a new retirement savings account. She wants to accumulate 1000000 dollars by the time she retires. Initially, Sharon deposits 5000 dollars into the account. She will make further deposits at the end of each month. The account will earn interest at annual rate 5 percent, compounded monthly.How much will she have to deposit into the account each month in order to reach this target after 30 years? (Give your answer, in dollars, correct to the nearest cent.)
2. Derek has just retired, and has 500000 dollars in his retirement account. The account will earn interest at an annual rate of 8 percent, compounded monthly. At the end of each month, Derek will withdraw a fixed amount to cover his living expenses. Derek wants his savings to last exactly 25 years. How much money can he withdraw each month? (Give your answer in dollars, correct to the nearest cent.) What is the maximum amount that Derek can withdraw each month if he wants his savings to last indefinitely?
Explanation / Answer
Answer-1:
Calculation of deposit into the account each month:
Total Future value required = $1000000
Intial deposit =$5000
Future value of $ 5000 after 30 years or 360 months at 5% per annum interest = 5000* (1+5%/12) ^360
=
22338.72
Hence Net future value required = 1000000 - 22338.72 = $977661.28
Using the formula of Future value of annuity :
Annuity = Future value / Future value annuity factor
Future value = $977661.28
Future value annuity factor (for 360 months at 5% / 12 rate ) = 832.26
Hence Amount to be deposited = 977661.28 / 832.26
=$1174.71
22338.72
Hence Net future value required = 1000000 - 22338.72 = $977661.28
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