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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.

Community
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Annie
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  • Please use $MathJax$ while posting anything here. –  Nov 02 '15 at 19:56
  • I think your reasoning looks correct. – paw88789 Nov 02 '15 at 20:01
  • If the inflation is $3%$, then the factor is $100%-3%=97%=0.97$. Therefore the future value in the first case is $10.000 \cdot (1.07\cdot 0.97)^7$. Beside this I would round up your result. So the answer is 7 years. – callculus42 Nov 02 '15 at 20:26
  • I've checked your answer and it's well done. The correct answer is more than 6 years. – alexjo Mar 04 '16 at 13:00
  • @callculus inflation means increase in price! so you have $+3%$. You'll have the minus sign in case of deflation (decrease of prices). – alexjo Mar 04 '16 at 13:02

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The answer as described by the OP is correct.

[Closing, but making community wiki so as not to take credit for another's answer.]

Avraham
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