Question

Jonathan and Sarah purchased a beach house for $10,000,000. The home appreciates at a rate of 3% per year. The appreciation of the house is shown in the graph. The home is currently worth about $13,000,000. Jonathan and Sarah have owned the home for about ______ years. how many years

Answer 1

current worth = 10,000,000 * (1.03)^years
We must determine the years when current worth = 13,000,000
13,000,000 / 10,000,000 = 1.03^years
1.3 = 1.03^years
Taking logs of both sides:
log (1.3) = years*log(1.03)
log(1.3) / log(1.03) = years
0.11394335231 / 0.012837224705 = years
years = 8.8760113598
Roughly about 8.9 years

Answer 2

13000000=10000000 (1+0.03)^t
Solve for t
T=log(13,000,000÷10,000,000)÷log(1+0.03)
t=8.9 years round 9 years