Principles of Finance - Compound Interest Calculations Present value (PV) of a single amount of 1 payable in n years at rate of interest is equal to Future value (FV) of a single amount of 1 payable in n years at rate of interest is equal to (1+1)" PV of an annuity of 1 p.a. payable annually in arrears (ie. payments are at year end ie 1.2...n) is 1-(1+1) PV of an annuity of 1 p.a. payable annually in advance Le payments are at year beginning Le. 0,1,2,...n- 1-(1+0 1) isi X (1 + i) FV of an annuity of 1 p.a. payable annually in arrears (i.e. payments are at year end i.e. 1,2,...n) is (1+0"-1 PV of an annuity of 1 p.a. payable annually in advance i.e. payments are at year beginning i.e. 0,1,2,.. (1+)-1 1) X(1 + i) 1. Find the PV of a single sum of $1,000 payable in 25 years at a rate of interest of 6% p.a. 2. Find the PV of an annuity payable in arrears of $1,000 p.a. payable for 25 years at a rate of interest of 6% p.a. 3. Find the PV of an annuity payable in advance of $1,000 p.a. payable for 25 years at a rate of Interest of 6% p.a. 4. Find the FV of an annuity payable in arrears of $1,000 p.a. payable for 25 years at a rate of interest of 6% p.a. 5. Find the FV of an annuity payable in advance of $1,000 p.a. payable for 25 years at a rate of Interest of 6% p.a. Effective and nominal rates of interest 10% payable twice years is really 5% p.a. which works out to 10.25% effective. The nominal rate Is 10%. If the question says the rate is a nominal rate payable then you just divide by the number of pay periods to get the effective rate per pay period. 6. Find the PV of an annuity payable in arrears of $1,000 p.a. payable quarterly for 25 years at an effective rate of interest of 6% p.a. 7. Find the PV of an annuity payable in arrears of $1,000 p.a. payable quarterly for 25 years at an nominal rate of interest of 6% p.a. compounded quarterly