Question 959172: Tom and Louise wants to establish an account that will supplement their retirement income beginning 30 years from now. Suppose they can invest in a fund that pays 6% interest compounded quarterly.
a. What is the lump sum they must deposit today so that $500,000 will be available at time of retirement if the account pays?
b. If they deposit $10,000 in the account now, how long would it take their money to double?
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! Tom and Louise wants to establish an account that will supplement their retirement income beginning 30 years from now. Suppose they can invest in a fund that pays 6% interest compounded quarterly.
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a. What is the lump sum they must deposit today so that $500,000 will be available at time of retirement if the account pays?
Compound Interest Formula: A=P(1+r/n)^nt, P=initial investment, r=interest rate, n=number of compounding periods per year, A=amount after t-years.
For given problem:
P=to find
r=.06
n=4
t=30
500000=P(1+.06/4)^(4*30)
500000=P(1+.015)^120
500000=P(1.015)^120
P=500000/(1.015)^120=83762
lump sum they must deposit today=$83,762
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b. If they deposit $10,000 in the account now, how long would it take their money to double?
A/P=2=(1+r/n)^nt
2=(1.015)^4t
take log of both sides
ln2=4t*ln(1.015)
t=ln2/4ln(1.015)=11.6
how long would it take their money to double? about 12 years
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