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
Shwetank Mauria
Apr 12, 2017

(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

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