Question

1.)You make a deposit of $46 each year for 40 years in an account that earns a simple interest rate of 6% per year. If you make the first deposit today, the future value of the deposits in 90 years will be:$___________

2.)How will you enter 10% in a computational formula (not in a financial calculator)?

3.)At what rate of interest will an amount triple in 50 years? Enter your answer as decimals, not percentages (e.g., enter 0.01 instead of 1%).

4.) In how many years will $150 become $300 if k=0.2% simple interest per year?

Answer 1

1) Interest for first deposit for 90 years = Principal * Rate * Time = 46*90*6%
Interest for second deposit for 89  years = Principal * Rate * Time = 46*89*6%
and so on
Interest for 40th deposit for years = Principal * Rate * Time = 46*50*6%
Total Interest = 46*6%*90*(90+1)/2 - 46*6%*40*(40+1)/2 = 9039
Total FV = 46*40+ 9039 = 10,879
Formula for total interest = Principal * Rate * n*(n+1)/2 - Principal * Rate *(n-40)*(n-39)/2

Total FV = Interest * number of payments + Total Interest

2) for 10%

Formula for total interest = Principal * Rate * n*(n+1)/2 - Principal * Rate *(n-40)*(n-39)/2 =
Principal * 10% * n*(n+1)/2 - Principal * 10% *(n-40)*(n-39)/2

Total FV = Interest * number of payments + Total Interest

3) Let principal = 100
Amount required = 3* 100 = 300
Time = 50
Amount = Principal + Principal * Rate * time/100
300-100 = 100* Rate * 50/100
Rate = 200/(50) = 4% or 0.04

4) Principal = 150
Amount = 300
Amount = Principal + Principal * Rate * Time/100 = 150 + 150*0.2*Time/100
300 = 150 + 150 *0.2* Time/100
150 = 150 *0.2*Time/100
Time = 100/0.2 = 500

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