The value of Alans stock portfolio grew by 20 in the first y

The value of Alan\'s stock portfolio grew by 20% in the first year, followed by a growth of 10% in the second year. It dropped 10% and 20% in the third and fourth years, respectively. Is the value of Alan\'s stock portfolio after 4 years the same as that when he started out?

Jada deposited an amount of money in a bank 3 years ago. If the bank had been paying interest at the rate of 6%/yearcompounded daily (assume a 365-day year) and she has $16,000 on deposit today, what was her initial deposit? (Round your answer to the nearest cent.)

Find the interest rate needed for an investment of $9,000 to grow to an amount of $12,000 in 6 years if interest is compounded daily. (Round your answer to the nearest hundredth of a percentage point.)

How long will it take for an investment of $5,000 to grow to $6,200 if the investment earns interest at the rate of8%/year compounded daily? (Round your answer to one decimal place.)

Solution

1) Let the value of stock be $100

grew by 20% in the first year --- 120% of 100 = $120

followed by a growth of 10% in the second year. 10% of $120 = (110/100)*120 = $ 132

It dropped 10% in third year = 90% 0f 132 =$ 118.8

dropped 20% in the fourth years = 80% 0f 118.8 = $ 95.04

So, we can see the value of stock is $ 95.04 as comared to $ 100 when he started.

2) Formula for compouding daily:

Amount = Principal( 1+ rate/365)^t*365

16000 = P ( 1+ 6/100*365 )^3*365

16000 = P*1.197

Principal = $ 13366.75 intial deposit