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Jack asked Jill to marry​ him, and she has accepted under one​ condition: Jack must buy her a new ​$ ​Rolls-Royce Phantom. Jack currently has ​$ that he may invest. He has found a mutual fund with an expected annual return of ​% in which he will place the money. How long will it take Jack to win​ Jill's hand in​ marriage?

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Answer: 47.8 years

Explanation:

Jack is trying to make up to $330,000 from $50,680 at a rate of 4%.

The relevant formula is the future value formula as Jack is trying to get to a certain amount in future:

330,000 = 50,680 * ( 1 + 4%) ^ number of years

1.04 ^ number of years = 330,000 / 50,680

1.04 ^ N = 6.51144435674822

Use the natural logarithm:

N * In (1.04) = In (6.51144435674822)

N * 0.039220713153281 = 1.873561299007586979

N = 1.873561299007586979 / 0.039220713153281

= 47.8 years

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