Question

Practice Question:

It has long been told that the French purchased Manhattan island in 1626 for the value of 60 guilders ($24). Assuming that the French invested this money into an account earning 5%, approximately how much would their investment be worth 380 years later in 2006?

A) $1.9 billion B) $2.7 billion C) $3.1 billion D) $4.5 billion

Answer 1

Solution :

The formula for calculating the future value of an Investment with compound Interest is

= P * ( 1 + (r/n) ) ^{n * t}

Where

P = Principal   ;   r = rate of interest   ; n = No. of compounding periods per year ; t = Time in years

As per the information given in the question we have

P = $ 24   ; r = 5 % = 0.05 ; n = 1   ;   t = 380    ;

Applying the above values in the formula we have

= $ 24 * ( 1 + ( 0.05 / 1 ) )^{(380 * 1)}

= $ 24 * ( 1 + 0.05 )³⁸⁰                                      

= $ 24 * ( 1.05 ) ³⁸⁰

= $ 24 * 112,702,525.11

= $ 2,704,860,602.73

= $ 2.7 Billion approximately

Thus the investment would be worth $ 2.7 Billion 380 years later in 2006.

The solution is Option B) $ 2.7 Billion

Note : ( 1.05 ) ³⁸⁰ = 112,702,525.11 is calculated using the excel formula =POWER(Number,Power)

=POWER(1.05,380)