Question

Christine O'Brien, who is self-employed, wants to investa. Choose the investment which will earn the most $80,000 in a pension plan. One investment offers 6% compounded quarterly. Another offers 5.75% compounded continuously. a. Which investment will earn the most interest in 5 years? b. How much more wil the better plan earn? C. What is the effective rate in each case? interest below O compounded continuously O compounded quarterly b. The difference is $ d. If Ms. O'Brien chooses the plan with continuous compounding, how long will it take for her $80,000 to grow to $90,000? e. How long will it take for her $80,000 to grow $90,000 if she chooses the plan with quarterly compounding? (Be careful; interest is added to the account only every quarter.) (Round to the nearest cent as needed.) c. The effective rate for investment compounded quarterly is 196. to at least (Round to the nearest hundredth as needed.) The effective rate for investment compounded continuously is! %. (Round to the nearest hundredth as needed.) d.years is needed to grow $80,000 to $90,000 with continuous compound interest. (Type an integer or a decimal rounded to the nearest hundredth.) e. years is needed to grow $80,000 to at least $90,000 with quarterly compound interest. (Type an integer or a decimal rounded to the nearest

Answer 1

Solution:

a)

Amount after 5 years if compounded quarterly

)"-$107748.4 AcompoundedQuarterly-80000 ( 1 + 400

ındedQuarterly-$107748.4-580000-$27748.4 Compou

Amount after 5 years if compounded continuously

AC ompoundedcontinuousty 80000e To5$107988.7

undedcontinuously $107988.7- $80000 $27988.7 Compo

So compounded continuously one gives more interest

$\text{b) }$

$\text{The difference is }\$240.3$

$\text{c)}$

0.06 rcom pounded Continous-e0.00-1-0.06183-6.183%

006)'- quite _ ( 1 = 0.06136 = 6.136'% 1 + I Compounded quarter

d)

$90000=80000e^{0.06t}$

0.06tS

$0.06t=\ln \frac{9}{8}$

$t=\frac{100}{6}\ln \frac{9}{8}=1.963\approx 2\text{ years}$