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Homework answers / question archive / Alma is planning to deposit $1,500 per year at ABC Bank for a period of 15 years, where the 15-year period is divided into 3 equal periods
Alma is planning to deposit $1,500 per year at ABC Bank for a period of 15 years, where the 15-year period is divided into 3 equal periods. The annual interest rate is expected to be 6% for the first period (year 1 to year 5), 10% for the second period (year 6 to year 10), then 14% for the last period (year 11 to year 15).
After that, Alma would like to deposit 40% of the interest earned from previous deposits in an investment with 8% return for a period of 4 years (year 16 to year 19). Find:
A.Total amount at the end of 15 years (In dollars)
B. Interest earned on deposits during the 19-year period (In dollars)
A=$1500
r=6%
n=5
FV of first five years at end of year 5= A*((1+r)^n-1)/r
=1500*((1+6%)^5-1)/6%
=1500*(1.06^5-1)/0.06
=1500*(1.3382-1)/0.06
=1500*0.3382/0.06
=$8455.64
FV of first five years at end of year 10=8455.64*(1+10%)^5=8455.64*1.1^5=8455.64*1.6105=$13617.89
FV of first five years at end of year 15= 13617.89*(1+14%)^5=13617.89*1.14^5=13617.89*1.9254=$26220.08
FV of 5 to 10 years at end of year 10= A*((1+r)^n-1)/r
=1500*((1+10%)^5-1)/10%
=1500*(1.1^5-1)/0.1
=1500*(1.6105)/0.1
=1500*0.6105/0.1
=$9157.65
FV of 5 to 10 years at end of year 15 =9157.65*(1+14%)^5=9157.65*1.14^5=9157.65*1.9254=$17632.27
FV of last five years at end of year 15= A*((1+r)^n-1)/r
=1500*((1+14%)^5-1)/14%
=1500*(1.14^5-1)/0.14
=1500*(1.9254-1)/0.14
=1500*0.9254/0.14
=$9915.16
Total FV at end of year 15=26220.08+17632.27+9915.16= $53767.51
total deposit =1500*15=$22500
Total interest earned=53767.51-22500=$31267.51
40% of interest =40%*31267.51=$12507
Amount at emd of year 19=12507*(1+8%)^4=12507.1.08^4=12507*1.3605=$17015.64
Interest earned in last 4 year=17015.64-12507=$4508.64
Total interest earned =31267.51+4508.64= $35776.15
