Bertie Frye saves $500 at the end of every quarter in an ordinary annuity earning 7.2% interest compounded quarterly. What is the amount if (a) his savings in $20 years and (b) how much interest will he have earned? If Bertie had saved the $500 at the beginning of each quarter in an annuity due, what would (c) the amount of savings be in 20 years and (d) how much interest would he have earned? a. b. c. d.
Bertie Frye saves $500 at the end of every quarter in an ordinary annuity earning 7.2% interest compounded quarterly. What is the amount if (a) his savings in $20 years and (b) how much interest will he have earned? If Bertie had saved the $500 at the beginning of each quarter in an annuity due, what would (c) the amount of savings be in 20 years and (d) how much interest would he have earned? a. b. c. d.
a- Bertie Frye will have saved in 20 years a total=$87,971.89
b-He will have earned=$87,971.89 - $40,000=$47,971.89 in interest.
c-If had saved at the beginning of each quarter, he would have=$89,555.38
d-He would have earned=$89,555.38 - $40,000=$49,555.38 in interest.
The formula you use to calculate this is:FV=P{[1 + R]^N - 1/ R}=FV OF $1 PER PERIOD,Where R=Interest rate per period, N=number of periods, P=periodic payment, FV=Future value.
7.2 % compounded QUARTERLY is equal to 7.2 / 4 = 1.8% each quarter period
In the first example, Bertie had nothing in her account for the first quarter, so in 20 YEARS she has deposits and interest for (20 x 4) - 1 = 79 quarters
F = A ( ( 1+i)^n -1)/i) Where i = 1.8 A = $500 n= number of periods (79 in this example) and F = how much she will have at the end of 20 years
In the SECOND example, she has 80 quarters of deposits and interest.....
same equation as above but n=80
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