I'm trying to solve the following question from a past SOA FM exam, but there are no posted solutions so I'm not sure if I'm headed in the right direction.
John deposits 10, 000 in a saving account which he assumes is paying 7% per annum interest effective. He has calculated that after 7 years he will be able to buy the hang glider he wants if its price inflates at a rate of 3% per annum effective. In fact the hang glider’s price inflates at only 1% per annum and the interest rate on the account is dropped to 5% per annum immediately after he makes the deposit. How many years does he have to wait for the hang glider?
P = Price of the hang glider
Under the old conditions of 7% per annum interest and inflation of 3% per annum effective:
$10,000 (1.07)^7 = P (1.03)^7$
$P = 13,056.47$
Under the new conditions of 5% per annum interest and inflation of 1% per annum effective, it'll take n years for John to save for the hand glider:
$10,000 (1.05)^n = 13,056.47 (1.01)^n$
$\left(\frac{1.05}{1.01}\right)^n = \left(\frac{13,056.47}{10,0000}\right)$
$n \times \ln\left(\frac{1.05}{1.01}\right) = \ln\left(\frac{13,056.47}{10,0000}\right)$
$n = 6.87$
So I get that it'll take over 6 years (which is one of the MPC answers). Any feedback? Thank you.
The answer as described by the OP is correct.
[Closing, but making community wiki so as not to take credit for another's answer.]