You deposited $5,000 from a late uncle on your 9th birthday. A) If you earned 10.5% interest each year, how much would you have when you turn 65?
B) If you earned 10.5% interest compounded monthly each year, how much would you have when you turn 65?
C) If you wanted to have $2 million when you turn 65, what rate of interest would you need to earn assuming annual compounding?

A) If you earned 10.5% interest each year, how much would you have when you turn 65?

assuming annual compounding:

future value = $5,000 x (1 + 10.5%)⁵⁶ = $1,340,471.47

B) If you earned 10.5% interest compounded monthly each year, how much would you have when you turn 65?

monthly compounding = 10.5% / 12 = 0.875% per month

future value = $5,000 x (1 + 0.875%)⁶⁷² = $1,743,869.89

C) If you wanted to have $2 million when you turn 65, what rate of interest would you need to earn assuming annual compounding?

$2,000,000 = $5,000 x (1 + r)⁵⁶

(1 + r)⁵⁶ = $2,000,000 / $5,000 = 400

(1 + r)⁵⁶ = 400

⁵⁶√(1 + r)⁵⁶ = ⁵⁶√400

1 + r = 1.1129

r = 1.1129 - 1 = 11.29%

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