You have just deposited $12,000 into an account that promises to pay you an annual interest rate of 6.7 percent each year for the next 8 years. You will leave the money invested in the account and 20 years from today, you need to have $44,950 in the account. What annual interest rate must you earn over the last 12 years to accomplish this goal?
FV after 8 Years = PV(1+r)^n
= $ 12000(1+0.067)^8
= $ 12000(1.067)^8
= $ 12000 * 1.6800
= 20160.28
FV after 20 Years = FV after 8 Years (1+r)^12
44950 = 20160.28 (1+r)^12
(1+r)^12 = 44950 / 20160.28
= 2.2296
1+r = 2.2296^(1/12)
= 1.0691
r = 1.0691 - 1
= 0.0691 i.e 6.91%
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