Question

You need to accumulate $10,000. To do so, you plan to make deposits of $1,250 per year - with the first payment being made a year from today - into a bank account that pays 15% annual interest. Your last deposit will be less than $1,250 if less is needed to round out to $10,000. How many years will it take you to reach your $10,000 goal? Do not round intermediate calculations. Round your answer up to the nearest whole number. year(s)

How large will the last deposit be? Do not round intermediate calculations. Round your answer to the nearest cent.

Answer 1

Answer : Calculation of Number of years :

Future Value of Annuity = Periodic Payment * Future Value of Annuity Factor @12% for n years

where n is the number of years we need to find out

10000 = 1250 * Future Value of Annuity Factor @15% for n years

==> Future Value of Annuity Factor @ 15% for n years = 10000 / 1250

= 8

By checking Future Value of Annuity Factor table @ 15% the value 8 at 12 percent interest rate lies approximately in 6 years.

Therefore Number of Years is 6

Alternatively ,

you can check Future value of Annuity by using Formula = [(1 + r)^n - 1] / r

= [(1 + 0.15)^6 - 1 ] / 0.15

=[2.31306076562 - 1] / 0.15

= 8.754

Therefore number of years is 6 years .

Amount of Last Deposit

Using Formula for future value of Annuity calculate value accumulated at the end of five years :

Future value of Annuity = Periodic Payment * {[(1 + r)^n - 1] / r}

where r is the rate of Interest per period i.e 0.15

n is the number of years i.e 5

Future value of Annuity = 1250 * {[(1 + 0.15)^5 - 1] / 0.15}

= 1250 * {[2.0113571875 - 1 ] / 0.15}

= 1250 * 6.74238125

= 8427.9765625

Future value after the interest in year 6 = 8427.9765625 * 1.15

= 9692.17304687

Amount to be deposited = 10000 - 9692.17304687

= 307.83