1. You should remember the formula of compound interest such that:
`A = P(1 + r/n)^(nt) `
A represents the amount of money accumulated
P represents the amount of money invested
t represents the number of years
n represents the number of times per year the interest is compounded
You need to substitute the given values in formula of compound interest such that:
`A = 5000(1 + 0.06/2)^(2t)`
`A = 5000*1.03^(2t)`
You may evaluate the amount of money accumulated after 1 year, two years, three years to write the geometric sequence `A_1,A_2,A_3` ,... such that:
`A_1 = 5000*1.03^2`
`A_2 =5000*1.03^4`
`A_3 =5000*1.03^6`
............................
Hence, evaluating the geometric sequence, using the formula of compound interest, yields `5000*1.03^2 , 5000*1.03^4 , 5000*1.03^6,...`
2. You need to substitute the given values in formula of compound interest such that:
`A = 10000(1 + 0.08/4)^(4t)`
`A = 10000*1.02^(4t)`
You may evaluate the amount of money accumulated after 1 year, two years, three years to write the geometric sequence `A_1,A_2,A_2` ,... such that:
`A_1 = 10000*1.02^4`
`A_2 = 10000*1.02^8`
`A_3 =10000*1.02^12`
............................
Hence, evaluating the geometric sequence, using the formula of compound interest, yields `10000*1.02^4 ,10000*1.02^8 , 10000*1.02^12,....`