Answer:
a. $231,839,557,939,952.9
b. $312,458,949,828,962
Step-by-step explanation:
Total number of years of investment = final year - initial year
= 2002- 1624 = 378 years;
Yearly rate of interest = 8%
Total investment made in 1624 is = $23
a) Interest when compounded quarterly
A = P ( 1 + r/t) ^tn where A = final amount; P = Principal amount' r= rate of interest per year; t = number of terms of compounding in a year; n = number of years
for quarterly compounding, t = 4 (as 4 times it gets compounded every year)
n = 378 years
P = $23
r= 8% or r= 0.08
Applying the formula we get:
A = 23 ( 1+ 0.08/4) ^4*378
A = 23* 10079980779997.95
A = $231,839,557,939,952.9
Therefore, with a quarterly compounding, this investment would come out to be $231,839,557,939,952.9
a) Interest when compounded quarterly
In continuous compounding
A = P * e^rt
P = $23
r= 8% or 0.08
t= 378 years
Substituting the values in the formula we get:
A = 23 ( e) 0.08*378
A= 23 (e) 30.24
A = 23 ( 13,585,171,731,694)
A = $312,458,949,828,962
Therefore, with a continuous compounding in place, 23$ investment, would amount to $312,458,949,828,962 by 2002.