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In: Accounting

3. a long time family friend owns a small business. this friend has promised to sell...

3. a long time family friend owns a small business. this friend has promised to sell you his business for $75,000 when he retires in 8 years. assuming that you can earn 7% on your money, how much will you need to save each year for the ext 8 years to have $75,000 when your friend retires?

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Expert Solution

Solution:
You need to save each year for the next 8 years to have $75,000 when your friend retires 7,310.08 in two decimal
7310 in whole number
Working Notes:
You need to save each next 8 years to have 75000 at end of 8th year i and you can earn 7% on your money , This question clearly is the question of Future value annuity. We have to find annual saving to get future value at end 8th year 75000 at interest rate of 7% p.a..
Future value of annuity formula
Future value of annuity = P x ((1+i)^n - 1)/i
P= saving per year =??
i=interest rate = 7%=0.07
n= no. Of years= 8 Year
Future value of annuity at end of 8th year = $75000
Future value of annuity at end of 8th year = P x ((1+i)^n - 1)/i
75,000 = P x ((1+0.07)^8 - 1)/0.07
P = 75,000/ (((1+0.07)^8 - 1)/0.07)
P = 75,000/ 10.25980257
P= $7,310.082187
P= $7,310.08
you need to save each year for the next 8 years to have $75,000 when your friend retires is $7,310.08
Please feel free to ask if anything about above solution in comment section of the question.

ekkarill92 answered 1 year ago
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