Deposit Annuities

1.

Michael invested $1000 per half-year in an IRA each half-year for 8 years earning 11% compounded semi-annually.
At the end of 8 years he ceased the IRA payments, but continued to invest his accumulated amount at 12% compounded yearly for the next 6 years.

a) What was the value of his IRA at the end of 8 years?

b) What was the value of the investment at the end of the next 6 years?



2.

(1 pt) Mike and Janet would like to have $22000 for a down payment on a house. Their budget only allows them to save $331.83 per month. How many years will it take them to save up the desired amount of $22000? Here we assume that their saving account will pay 4% compounded monthly.



3.

(1 pt) A company borrows $160000, which will be paid back to the lender in one payment at the end of 6 years. The company agrees to pay yearly interest payments at the nominal annual rate of 7% compounded yearly. At the same time the company sets up a sinking fund in order to repay the loan at the end of 6 years. The sinking fund pays interest at an annual nominal interest rate of 15% compounded yearly. Find the total amount of the yearly payments, that is, the sum of the interest payment and the sinking fund payment.

 

From wiki, the compound interest formula

Formula for calculating compound interest:



Where,

* A = final amount
* P = principal amount (initial investment)
* r = annual nominal interest rate (as a decimal)
* n = number of times the interest is compounded per year
* t = number of years

Should be simple plugging in and getting answers.



The only thing you have to watch out for is when they say compounded continuously. This means that n would be infinity so you need to set up a limit.

 

Take help from cash for annuities. Its extremely helpful specially for annuity calculations. I personally often refer this.