13. In the following ordinary annuity, the interest is compounded with each paym
ID: 2737618 • Letter: 1
Question
13. In the following ordinary annuity, the interest is compounded with each payment, and the payment is made at the end of the compounding period.Find the amount of time needed for the sinking fund to reach the given accumulated amount. (Round your answer to two decimal places.) $5500 yearly at 7% to accumulate $100,000.
Yr
14. In the following ordinary annuity, the interest is compounded with each payment, and the payment is made at the end of the compounding period. An individual retirement account, or IRA, earns tax-deferred interest and allows the owner to invest up to $5000 each year. Joe and Jill both will make IRA deposits for 30 years (from age 35 to 65) into stock mutual funds yielding 9.6%. Joe deposits $5000 once each year, while Jill has $96.15 (which is 5000/52) withheld from her weekly paycheck and deposited automatically. How much will each have at age 65? (Round your answer to the nearest cent.)
Joe
Jill
15. In the following ordinary annuity, the interest is compounded with each payment, and the payment is made at the end of the compounding period. How much must you invest each month in a mutual fund yielding 11.5% compounded monthly to become a millionaire in 10 years? (Round your answer to the nearest cent.)
$
16. Calculate the present value of the annuity. (Round your answer to the nearest cent.) $16,000 annually at 5% for 10 years.
$
Explanation / Answer
13.A = Pert
100000 = 5500e7t
e7t = 100000/5500 (A/P)
e7t = 18.18
ln(A/P) = ln(ert) Applying the "power rule" for logarithms to the right side: ln(x)n = n.ln(x) and recalling ln(e)=1, that you can simplify the right side to:
ln(18.18) = ln(e7t)
ln(18.18) = 7t(1) Divide both sides by r.
ln(18.18) / r = t
ln(18.18) / 0.07 = t
log 18.18 = 1.26
therefore,
1.26/0.07 =t
18 = t
t = 18 years.
14. In case of Joe,
An = (1 + i)n P
A = (1+ 0.096)30 5000
A = (1.096)30 5000
A= 15.64 * 5000 since (1.096)30 = 15.64
A = $78200
Joe will have $78200 at the age of 65 years.
In case of Jill,
An = (1 + i)n P
A = (1+ 0.096)30 96.15
A = (1.096)30 96.15
A= 15.64 * 96.15 since (1.096)30 = 15.64
A = $1503.79 i.e. $1504
Jill will have $1504 at the age of 65 years.
15. i = 10%
i12 = 9.5690% i.e. 0.095690
accumulating factor after 10 years = Present value (PV) [1+(0.095690/12)]12*10
we know, accumulating factor after 10 years = 1 million = $1000000
according to problem, 1000000 = Present value (PV) [1+(0.095690/12)]12*10
or, PV = 1000000 / [1+(0.095690/12)]12*10
or, PV = 1000000 / [1+0.007974]120
or, PV = 1000000 / [1.007974]120
or, PV = 1000000 / 2.59375 since, [1.007974]120 = 2.59375
PV = $385542.1687 i.e. $385542
therefore, $385542 will be invested each month in a mutual fund to become a millionaire in 10 years.
16. PMT = PV [(1-1/(1+i)n) / i ]
16000 = PV [(1-1/(1+0.05)10) / 0.05] here, i= 5% i.e. 0.05% ;n = 5 years
PV = 16000/[(1-1/(1.05)10) / 0.05]
PV = 16000/ [(1-1/1.63) / 0.05]
PV = 16000/ [(1-0.61) / 0.05]
PV = 16000/ [0.39 / 0.05]
PV = 16000/7.8
PV = $2051.28 i.e. $2051
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.