Question

At the beginning of each year, you are paid 2,000 that goes into an account that earns interest at a rate of 5% per year. These deposits must remain in this account until eight years have passed. You deposit the interest earned by this account into a secondary account that earns interest at a rate of 8% per year. What is the total accumulated value in your accounts when eight years have passed?

Answer 1

Account 1:

Amount received = $2,000 p.a.

Interest earned = 5% p.a. = $100 (which is transferred into account 2)

As all the interest is transferred to the account 2, only the principle amount will remain in account 1.

Total Accumulated value in this account in 8 years = $2,000 * 8 = $16,000

Account 2:

Amount received at the end of year 1 = $100

Interest earned in this account = 8% p.a.

FV after 8 years = Amount * {(1 + rate)years -1}/rate = $100 *{(1+8%)8 - 1} / 8% = $1,063.66 ~ $1,064

Total amount in both the accounts by the end of 8th year:

Account 1 + Account 2 = $16,000 + $1,064 = $17,064