In 1624, an explorer convinced a group of indigenous peoples to sell him an island for $ 23. If the indigenous peoples had put the $ 23 into a bank account paying 8 %, how much would the investment be worth in the year 2002 if the interest were compounded a. quarterly? b. continuously?

a. $231,839,557,939,952.9

b.  $312,458,949,828,962

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.