Reaching a Financial Goal You need to accumulate $10,000. To do
so, you plan to make deposits of $1,000 per year - with the first
payment being made a year from today - into a bank account that
pays 7.15% annual interest. Your last deposit will be less than
$1,000 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. $__________
Number of years (n)
FV = 10,000
PMT = 1000
Rate = 7.15%
FV = PMT*((1+r)n-1)/r
10,000 = 1000 *((1+7.15%)n-1)/7.15%
10*7.15% = (1+7.15%)^n-1
1.715 = (1+7.15%)^n
Applying log on both sides =
n = log 1.715/log 1.0715= 7.81 years
FV of annuity in 7 years = 1000*((1+7.15%)7-1)/7.15% =
8693.78
Value of 10,000 in year 7 = 10,000/1.0715 = 9332.71
The Last deposit = 9332.71 - 8693.78 = 638.93
Please Discuss in case of Doubt
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