An amount say #$800# is invested at a rate of interest of #5%# for #30# years. What is the amount at the end of the period if it is?

(a) compounded every year
(b) compounded monthly
(c) compounded every week
(d) compounded continuously.

1 Answer
Apr 12, 2017

Answer:

(a) #$3457.55# (b) #$3574.20#
(c) #$3582.77# (d) #$3585.35#

Explanation:

When we invest an amount say #P# at a rate of interest of #r# for #t# years, the amount at the end of the period (at simple interest) becomes #P(1+(rt)/100)#.

However, when compounded, it depends on the fixed period after which it is compounded or rather how many times in a year interest is compounded. If it is compounded after every #1/n# year,

the amount becomes #P(1+r/(nxx100))^(nt)#

Here we have #P=$800#, #r=5%# and #t=30# years

(a) If compounded yearly i.e. once a year, as #n=1#, it becomes

#800(1+5/100)^30=800xx1.05^30=800xx4.321942=$3457.55#

(b) If compounded monthly i.e. #12# times a year, as #n=12#, it becomes

#800(1+5/1200)^(30xx12)=800xx1.004166^360=800xx4.467744=$3574.20#

(c) If compounded weekly i.e. #52# times a year, as #n=52#, it becomes

#800(1+5/5200)^(30xx52)=800xx1.00096154^1560=800xx4.47846=$3582.77#

(d) If compounded continuously, it approximates #Pe^((rt)/100)# i.e.

#800e^((5xx30)/100)=800xxe^1.5=800xx4.481689=$3585.35#