Question

Suppose you can afford $15,600 per year to invest into a savings annuity. Write this value down, as you'll be using it throughout this entire problem. We are going to explore various options and how these options will impact the interest you are making.

Rate

r = 5.3%

If you are making monthly deposits from your available funds, what is the total value in your annuity at the end of 30 years, given the rate is 5.3%? $ _____

How much interest did you earn? $ _____

r = 5.8%

If you are making monthly deposits from your available funds, what is the total value in your annuity at the end of 30 years, given the rate is 5.8%? $ ____

How much interest did you earn? $ _____

r = 6.3%

If you are making monthly deposits from your available funds, what is the total value in your annuity at the end of 30 years, given the rate is 6.3%? $ _____

How much interest did you earn? $ _____

Time

25 years

If you make monthly deposits at an annual rate of 5.3%, what is the total value in the account after 25 years? $ _____

How much interest did you earn? $ _____

30 years

If you make monthly deposits at an annual rate of 5.3%, what is the total value in the account after 30 years? $ _____

How much interest did you earn? $ ______

35 years

If you make monthly deposits at an annual rate of 5.3%, what is the total value in the account after 35 years? $ _____

How much interest did you earn? $ _____

40 years

If you make monthly deposits at an annual rate of 5.3%, what is the total value in the account after 40 years? $ _____

How much interest did you earn? $ _____

Conclusion

Which factor had the greatest impact on the amount of interest that you earned? Payment frequency, rate, or time

Answer 1

Computation of future value from regular monthly deposit

Pn = R((1+r)^n-1)/r

Pn is future value of investment

R is making monthly deposit= yearly deposit = $15,600 so monthly deposit would be 15,600/12 =$1,300

r= interest rate per period

n is the number of period

Particulars	Formula	Future Value	Total deposit	Interest=( Future value - Total deposit)
A) R= $1,300 n = 30yrs× 12 = 360 r= 5.3% or 0.053/12 (Monthly interest)	P(30 @5.3%)= $1300((1+0.053/12)^360-1) / (0.053/12) =$1,300((1.0044166)^360-1)/0.0044166 =$1,143,983.67	$1,143,983.67	monthly deposit× n =$1,300× 360 =$468,000	$1,143,983.67-$468,000 = $675,983.67
B) R =$1,300 n= 30×12=360 r= 5.8% or 0.058/12	P([email protected]%) = $1,300((1+0.058/12)^360-1)/(0.058/12) =$1,257,013.84	$1,257,013.84	=$1,300×360 =$468,000	$1,257,013.84-$468,000 =$789,013.84
C) r=6.3% or 0.063/12 n = 30×12 = 360 R=$1,300	P ([email protected]%)= $1,300((1+0.063/12)^360-1)/(0.063/12) =$1,383,379.18	$1,383,379.18	$1,300×360 =$468,000	$1,383,379.18- S468,000 =$915,379.18
TIME
D) R=1,300 n = 25yrs × 12 = 300 r= 5.3% or 0.053/12	P([email protected]% )= $1,300((1+0.053/12)^300-1)/ (0.053/12) =$809,697.014	$809,697.014	$1,300× 25× 12 = $390,000 (25year monthly payment )	$809.697.014-390,000 =$419,697.014
E) R = $1,300 n = 30year × 12 = 360 r = 5.3% or 0.053/12	P ( [email protected]%) =$1,300((1+0.053/12)^360-1)/(0.053/12) =$1,143,983.67	$1,144,983.67	$1,300× 30×12 = $468,000	$1,144,983.67-$468,000 =$675,983.67
F) R=$1,300 n= 35years × 12= 420 r = 5.3% or 0.053/12	P([email protected]%) =$1,300((1+0.053/12)^420-1)/ (0.053/12) =$1,579,321.93	$1,579,321.93	$1300× 35×12 = $546,000	$1,579,321.93-$546,000 =$1,033,321.9
G) R=$1,300 r = 5.3% or 0.053/12 n= 40years × 12= 480	P([email protected]%) = $1,300((1+0.053/12)^480-1) / (0.053/12) =$2,146,424.3	$2,146,424.3	=$1,300× 40×12 = $624,000	= $2,146,424.3-$624,000 =$1,522,424.3

High rate and long time duration are the two main factor for greater impact on Interest Earned.