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Question 1162034: Frank received a 380,000 dollar inheritance on his 30th birthday and invested it into a fund that earns 5.3%, compounded semiannually. If this amount is deferred until Frank’s 60th birthday, how much will it provide at the end of each half-year for the next 10 years?
Found 2 solutions by solver91311, Theo:
Answer by solver91311(24713)   (Show Source):
Answer by Theo(13342)  (Show Source):
You can put this solution on YOUR website! frank received 380,000 dollars on his 30th birthday.
he invest it at 5.3% compounded semi-annually until his 60th birthday.
how much will it provide at the end of each half year for the next 10 years (until his 70th birthday).
first you need to get the future value of 300,000 for 30 years.
formula is f = p * (1 + r) ^ n
f is the future value
p is the present value
r is the interest rate per time period.
n is the number of time periods.
formula becomes:
f = 380,000 * (1 + .053/2) ^ (30 * 2) = 1,825,243.5326.
.053/2 is the interest rate per half year.
30 * 2 is the number of half years.
380,000 is the present value.
at the end of the 30 year period, he has 1,825,24.536 to draw from at the end of each half year for the next 10 years.
the formula to use is the annuity from a present value formula with end of time period payments.
that formula is shown below:
ANNUITY FOR A PRESENT AMOUNT WITH END OF TIME PERIOD PAYMENTS
a = (p*r)/(1-(1/(1+r)^n))
a is the annuity.
p is the present amount.
r is the interest rate per time period.
n is the number of time periods.
that formula becomes:
a = (1825243.536*.053/2)/(1-(1/(1+.053/2)^(10*2))) = 118,749.5326.
the future value from the first formula becomes the present value in the second formula.
the interest rate is still .053/2.
the number of time periods becomes 10*2.
he will be able to draw 118,749.5326 at the end of each half year period for the next 10 years until he's 70.
you could have solved this using a financial calculator as well.
here are the results from using the financial calculator online at https://arachnoid.com/finance/index.html
this calculator requires percent, not rate.
if the present value is entered as negative, the future value comes out at positive.
the time periods have to be specific, i.e. 60 rather than 30/2 or 20 rather than 20/2.
the interest rate has to be specific, i.e. 2.65 rather than 5.3/2.
the first use of the calculator finds the future value.
that future value becomes the present value in the second use of the calculator.
10 years * 2 is entered as 20 in the second use of the calculator.
the present value is entered as negative and the payment per time period comes out positive.
you get the same answer whether you use the calculator or the formula, as you should.
this calculator, however, rounds your answers to the nearest penny.
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