annuity question

Question

Lincoln Benefit Life LLC offers an annuity that has a fixed annual interest
rate of 5.5%, and interest is compounded quarterly.
(a) What equal quarterly deposit should be made into this annuity at the end of each
quarter in order to have $50,000 after making 5 years of payments?
(b) How much interest do you earn?

Answer 1

Hi Felesi,

 

The question is about ordinary annuity because deposits are made at the end of each quarter. We are given with

Financial goal or future value of ordinary annuity = $50,000

interest rate  = 5.5% compounded quarterly

time = 5 years

total number of payments = number of payments in a year * the number of years = 4*5 = 20

Quarterly deposit =?

interest = ?

 

The formula that helps us to get the payments in future value of ordinary annuity is 

 

You put your given items in a financial calculator, web calculator or your future value of ordinary annuity table. The following page may help you get the figures below.

 

http://www.ultimatecalculators.com/future_value_annuity_calculator.html

 

Quarterly deposit = $1,433.97.  I get this by substituting the above values in the web calculator you can get in the above link

 

Interest = Future value of the annuity - total out-of-pocket deposits

             = 50,000.00 - ($1,433.97*20)

             = $21,320.60

 

I hope it helps.

A.