# Calculating the Time Value of Money

Hi, I need assistance with the following calculations:

1. Calculate the future value of the following:

Future value= Present value *(1+rate of interest) ^ duration

a) $190,537.19 if invested for six years at a 8% interest rate

=190,537.19*(1+8%) ^6

=$

b) $231,891.22 if invested for four years at a 9% interest rate

=231,891.22*(1+9%) ^4

=$

c)$310,891.12 if invested for nine years at an 5% interest rate

=310,891.12*(1+5%) ^9

=$

d) $420,520.22 if invested for fifteen years with a 1% interest rate

=420,520.22*(1+1%) ^15

=$

2. Calculate the present value of the following:

Present value= Future value / (1+rate of interest) ^ duration

a) $552,126.17 to be received four years from now with a 3% interest rate

=552,126.17/ (1+3%) ^4

=$

b)$125,003.21 to be received three years from now with an 8% interest rate

=125,003.21/ (1+8%) ^3

=$

c)$621,567.35 to received nine years from now with a 14% interest rate

=621,567.35/ (1+14%) ^9

=$

d)$93,000.05 to be received eleven years from now with a 2% interest rate

=930,000.05/ (1+2%) ^11

=$

3. Suppose you are to receive a stream of annual payments (also called an "annuity") of $225,891.12 every year for five years starting at the end of this year. The interest rate is 7%. What is the present value of these five payments?

4. Suppose you are to receive a payment of $337,891.24 at the end of each year for seven years. You are depositing these payments in a bank account that pays 6% interest. Given these seven payments and this interest rate, how much will be in your bank account in seven years? Note: This is the compounded value of annuity.

#### Solution Preview

Dear Student:

1. Future value= Present value *(1+rate of interest) ^ (number of years)

a. Future value of $190,537.19 if invested for six years at a 8% interest rate

=190,537.19*(1+8%) ^6 = 190,537.19 * (1.08)^6 = 190,537.19 * 1.58687432294 = $302,358.57

b. Future value of $231,891.22 if invested for four years at a 9% interest rate

=231,891.22*(1+9%) ^4 =231,891.22 * (1.09)^4 = 231,891.22 * 1.4115811 = $327,333.38

c. $310,891.12 if invested for nine years at an 5% ...

#### Solution Summary

This solution shows detailed calculations using time value of money and assuming compound interest. (1) Calculating the future value of a present value lump-sum when invested for different number of years and interest rates. (2) Calculating the present values when future values are given. (3) Calculating the present value of a 5-year annuity. (4) Calculating the future value of a 7-year annuity.