You need to accumulate $10,000. To do so, you plan to make deposits of $1,950 per year - with the first payment being made a year from today - into a bank account that pays 8.05% annual interest. Your last deposit will be less than $1,950 if less is needed to round out to $10,000. How many years will it take you to reach your $10,000 goal? How large will the last deposit be?
Number of years (n)
FV = 10,000
PMT = 1950
Rate = 8.05%
FV = PMT*((1+r)n-1)/r
10,000 = 1950 *((1+8.05%)n-1)/8.05%
1.0805n = 1.4128
Applying log on both sides = log 1.0805n = log
1.4128
n = log 1.4128/log 1.0805= 4.46 years
FV of annuity in 4 years = 1950*((1+8.05%%)4-1)/8.05% =
8793.41
Value of 10,000 in year 4 = 10,000/1.0805 = 9254.97
The last deposit value = 9254.97 - 8793.41 = 461.56
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