You just won $50,000 in a lottery. You want to use the money to make a down paym
ID: 2737951 • Letter: Y
Question
You just won $50,000 in a lottery. You want to use the money to make a down payment on a house 5 years from now. Meanwhile you want to invest it to accumulate more funds. Bank of USA advertises that they pay 6% per year compounded monthly on a five-year investment, but they charge an administrative fee that is 2% of the amount invested and this has to be paid initially to the bank. First American Credit Union offers 5.75% compounded daily on a money market account. Which investment would you choose and why? Assume that there is no risk associated with either investment!
Explanation / Answer
Answer:
We need money at the end of 5 years & we have two options for investment. We will use future value of money concept to solve this question.
Option to invest in American Credit Union,
Future value of money formula for compunding on daily basis = Amount x (1 + Interest rate/365days) years x 365 days
Future value of money = $ 50,000 x(1 + 5.75%/365days)1825 days
Future value of money = $ 50,000 x(1 + 0.000158)1825 days
Future value of money = $ 50,000 x 1.339072
Future value of money = $66,953.59
So, if we invest $ 50,000 today in American credit union option, we will get $ 66,953.59 at the end of 5th year.
Option to evaluate in Bank of USA
Bank of USA charges 2% administrative fees upfront, so we have to pay ($50,000 x 2%) = $ 1000 upfront fees. After deducting administrative fees, we will be able to invest only $ 49,000 under this option.
Future value of money formula for compunding on quarterly basis = Amount x (1 + Interest rate/4 Quarter) years x 4 Quarter
Future value of money = $ 49,000 x (1 + 6%/4 )5 years x 4 Quarter
Future value of money = $ 49,000 x (1 + 0.015 )20
Future value of money = $ 49,000 x 1.346855
Future value of money = $ 65,995.90
So, after evaluating both option, we should invest in American credit Union option because we will get more money by investing in this option.
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