Question

When Da Vinci's first airplane model was sold at auction in 1895, it went for $230. In 2016, the original owner sold the paininting again and this time Sotheby's auctioneers were able to sell it for the staggering sum of $1,450,000.

a. What was the annual percentage increase in price of the painting over this period? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

b. How much money should the painting be worth in 2030 if the price of the painting increases at the same rate as (a)? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Answer 1

We use the formula:  
A=P(1+r/100)^n
where   
A=future value
P=present value  
r=rate of interest
n=time period.

a.1,450,000=230*(1+r/100)^121

(1,450,000/230)^(1/121)=(1+r/100)

(1+r/100)=1.075

r=1.075-1

=7.5%(Approx)

b.A=1,450,000*(1.075)^14

=$3,990,210.34(Approx)