In: Finance
A.Calculate the present value of an annuity of $5,000 received annually that begins today and continues for 10 years, assuming a discount rate of 9%.
B. Joan invested $5,000 in an interest-bearing account earning an 8% annual rate of interest compounded monthly. How much will the account be worth at the end of 5 years, assuming all interest is reinvested at the 8% rate?
C. Calculate the present value of an ordinary annuity of $5,000 received annually for 10 years, assuming a discount rate of 9%.
D. Calculate the future value of $10,000 invested for 10 years, assuming an annual interest rate of 9%.
E. Calculate the present value of $10,000 to be received in exactly 10 years, assuming an annual interest rate of 9%
A. | Present Value of Annuity | $ 34,976.23 | |||||||||
Working: | |||||||||||
Present Value | = | Annuity x Present Value of annuity due of $ 1 | |||||||||
= | $ 5,000.00 | x | 6.995 | ||||||||
= | $ 34,976.23 | ||||||||||
Present Value of annuity due of $ 1 | = | ((1-(1+i)^-n)/i)*(1+i) | Where, | ||||||||
= | ((1-(1+0.09)^-10)/0.09)*(1+0.09) | i | 0.09 | ||||||||
= | 6.995 | n | 10 | ||||||||
B. | Value of investment at the end of 5 years | $ 7,464.04 | |||||||||
Working: | |||||||||||
Future Value | = | P*(1+i)^n | Where, | ||||||||
= | 5000*(1+0.0067)^60 | i | 8%/12 | = | 0.0067 | ||||||
= | $ 7,464.04 | n | 5*12 | = | 60 | ||||||
P | = | $ 5,000 | |||||||||
C. | Present Value | $ 32,088.29 | |||||||||
Working: | |||||||||||
Present Value of ordinary annuity | = | Annuity x Present Value of ordinary annuity of $ 1 | |||||||||
= | $ 5,000.00 | x | 6.418 | ||||||||
= | $ 32,088.29 | ||||||||||
Present Value of ordinary annuity of $ 1 | = | (1-(1+i)^-n)/i | Where, | ||||||||
= | (1-(1+0.09)^-10)/0.09 | i | 0.09 | ||||||||
= | 6.418 | n | 10 | ||||||||
D. | Future Value | $ 23,673.64 | |||||||||
Working: | |||||||||||
Future Value | = | P*(1+i)^n | Where, | ||||||||
= | 10000*(1+0.09)^10 | P | $ 10,000 | ||||||||
= | $ 23,673.64 | i | 0.09 | ||||||||
n | 10 | ||||||||||
E. | Present Value | $ 4,224.11 | |||||||||
Working: | |||||||||||
Present Value | = | F*(1+i)^-n | Where, | ||||||||
= | 10000*(1+0.09)^-10 | F | $ 10,000 | ||||||||
= | $ 4,224.11 | i | 0.09 | ||||||||
n | 10 | ||||||||||