Financial Applications -Annuities (Accumulated Amount) Choi

Annuities An annuity is a sequence of equal payments made at equally spaced intervals of time. The period of an annuity is the time interval between two consecutive payments. The term of an annuity is the total time involved in completing the annuity. Ordinary annuities have payments made at the end of the payment period.

Recall: Compound Interest formula The formula used in compound interest is Amount (A) . Principal (P) Interest rate per period (i) Number of compounding periods involved (n)

Annuities formula Amount of annuity (A) . Regular activity (R) The formula to calculate the accumulated amount with annuities is: Amount of annuity (A) . Regular activity (R) Interest rate per period (i) Number of compounding periods involved (n)

Example 1 – Annuities Lisa plans to deposit $500 at the end of the year for 5 years in a special saving account. If the account pays interest at the rate of 9% compounded annually, what will be the accumulated amount at the end of 5 years? Using the Annuities Formula Now 1 5 4 3 2 $500 $500 $500 $500 $500 Geometric Series with: Therefore, the accumulated amount at the end of 5 years is $2992.36

Example 2 – Annuities An annuity of semi-annual payments of $3000 is for 4 years at 10% per annum compounded semi-annually. If the first payment is in 6 months time, what is the amount of the annuity? Now 1 4 3 2 $3000 $3000 $3000 ...... $3000 $3000 ...... We want to find the accumulated value in the future!!  A Therefore, the accumulated amount at the end of 4 years is $28647.33

RBC Investing Promotions 2017 So what is the annual interest rate???

RBC Investing Promotions 2017 Now 1 260 259 2 $25 $25 ...... $25 $25 ...... r= 0.045 4.50% per year i= 0.000865385 0.0865% per week 1.255461538 1.252200872 1+295.2i (1+i)^260

Example 3 – Annuities Henry plans to make an equal deposit at the end of each year for 10 years in a trust account that pays interest at 12% compounded annually. If he expects to have $100 000 at the end of 10 years, what must be his annual deposit? Now 1 10 3 2 ...... 9 8 x x x ...... x x x ...... The accumulated value of x will become an amount in the future!!  A Therefore, the annual deposit is $5698.42

Example 4 – Annuities Tommy is in Grade 10 now and he plans to buy his first car in 3 years when he is going into university. If his budget for a used car is $16000 and he needs to prepare 25% for the down payment and plans to finance for the remaining parts for 4 years. How much he needs to save per month into his bank that pays 2.4% per annum compounded monthly in order to reach his plan for the down payment? The accumulated value of x will become 25% of $16000 in the future!!  A Therefore, he needs to save up $107.27 per month.

Homework: WS: Single Payments and Annuities