1.TIME TO REACH A FINANCIAL GOAL You have $56,930.69 in a brokerage account, and
ID: 2808659 • Letter: 1
Question
1.TIME TO REACH A FINANCIAL GOAL
You have $56,930.69 in a brokerage account, and you plan to deposit an additional $3,000 at the end of every future year until your account totals $260,000. You expect to earn 12% annually on the account. How many years will it take to reach your goal? Round your answer to two decimal places at the end of the calculations.
years
2. FUTURE VALUE: ANNUITY VERSUS ANNUITY DUE
What's the future value of a 3%, 5-year ordinary annuity that pays $200 each year? Round your answer to the nearest cent.
$
If this was an annuity due, what would its future value be? Round your answer to the nearest cent.
$
Explanation / Answer
1.
We use the formula:
A=P(1+r/100)^n
where
A=future value
P=present value
r=rate of interest
n=time period.
Hence A for $56,930.69= $56,930.69*(1.12)^n
Also:
Future value of annuity=Annuity[(1+rate)^time period-1]/rate
=$3000[(1.12)^n-1]/0.12
260,000=$56,930.69*(1.12)^n+$3000[(1.12)^n-1]/0.12
260000=$56,930.69*(1.12)^n+$25000[(1.12)^n-1]
260000=$56,930.69*(1.12)^n+$25000(1.12)^n-25000
(260,000+25000)=(1.12)^n[56,930.69+25000)
(260,000+25000)/[56,930.69+25000]=(1.12)^n
(1.12)^n=3.478549979
Taking log on both sides;
n*log 1.12=log 3.478549979
n=log 3.478549979/log 1.12
=11 years.
2.
a.Future value of annuity=Annuity[(1+rate)^time period-1]/rate
=$200[(1.03)^5-1]/0.03
=$200*5.30913581
=$1061.83(Approx).
b.Future value of annuity due=Future value of annuity*(1+interest rate)
=$1061.83*1.03
=$1093.68(Approx).
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