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Reaching a Financial Goal You need to accumulate $10,000. To do so, you plan to make...

Reaching a Financial Goal

You need to accumulate $10,000. To do so, you plan to make deposits of $1,900 per year - with the first payment being made a year from today - into a bank account that pays 10.7% annual interest. Your last deposit will be less than $1,900 if less is needed to round out to $10,000. How many years will it take you to reach your $10,000 goal? Round your answer up to the nearest whole number.
year(s)

How large will the last deposit be? Round your answer to the nearest cent.
$

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Answer #1

Number of years (n)
FV = 10,000
PMT = 1900
Rate = 10.7%

FV = PMT*((1+r)n-1)/r
10,000 = 1900 *((1+10.7%)n-1)/10.7%
1.107n = 1.5632
Applying log on both sides = log1.107n = log1.5632
n = log 1.5632/log1.107 = 4.39 years

FV of annuity in 4 years = 1900*((1+10.7%)4-1)/10.7% = 8909.14
Value of 10,000 in year 4 = 10,000/1.107 = 9033.42

The last deposit value = 9033.42 - 8909.14 = 124.28

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