Question

Find the periodic payments PMT necessary to accumulate the given amount in an annuity account. (Assume end-of-period deposits and compounding at the same intervals as deposits. Round your answer to the nearest cent.)$10,000 in a fund paying 7% per year, with monthly payments for 10 years PMT = $ When I was considering what to do with my $10,000 lottery winnings, my broker suggested that I invest half of it in gold, the value of which was growing by 9% per year, and the other half in certificates of deposit (CDs), which were yielding 6% per year, compounded every 6 months. Assuming that these rates are sustained, how much will my investment be worth in 12 years? (Round your answer to the nearest cent.) $

Answer 1

equation to find future value of ordinary annuity (end of period) is

$\large future \;value=PMT\left [ \frac{(1+r)^n-1}{r} \right ]$

here PMT is monthly payment . r is intersest rate per month in decimal. if Apr is given , then r= Apr/1200

n is total number of months.

here we need 10000 in future . so future value is 10000 . Apr is 7% . so r=7/1200

10 years . so n=10*12=120

apply this values and find PMT

(1 + 1200120 1 10000 = PMT = PMT * 173.0848074 1200

$\large PMT=\frac{10000}{173.0848074}=57.77514589\approx 57.78$

so answer is PMT = 57.78

5000 is invested in 5000 invested in gold and 5000 invested in CD

equation to find future value of compound investment is

$\large A=P(1+\frac{r}{n})^{nt}$

here P is amount invested, r is rate of interest in decimal per year , t is number of years and n is number of compounding .

for gold investment P=5000 , r=0.09 ,t=12 ,n=1 . so value of investment after t years is

$\large A=5000(1+\frac{0.09}{1})^{1*12}=14063.32$

for CD investment P=5000 . r=0.06 ,t=12 . compunding is 2 times an year . so n=2

so

$\large A=5000(1+\frac{0.06}{2})^{2*12}=10163.97$

so total value of this investment is 14063.32+10163.97=24227.29

so answer is 24227.29