You put $10000 in an account earning 5%. After 3 years, you make another deposit into the same account. Four years later (7 years after initial $10000) the account balance is $20000. What was the amount of the deposit at the end of year 3

You put $10000 in an account earning 5%. After 3 years, you make another deposit into the same account. Four years later (7 years after initial $10000) the account balance is $20000. What was the amount of the deposit at the end of year 3

Answer:money deposited after end of 3rd year is $4877.75Explanation:given data

initial amount = $10000

rate = 5%

time = 3 year

after 7 year account balance = $20000

solution

we consider here money deposited after end of 3rd year is = x

first we get here compounded amount after 3 years as

compounded amount = initial amount × [tex](1+r)^{t}[/tex] …………….1

compounded amount = 10000 × [tex](1+0.05)^{3}[/tex]

compounded amount = $11576.25

so at 7 year account balance is

account balance = ( compounded amount + x ) × [tex](1+r)^{t}[/tex] ………………..2

$20000 = ( $11576.25 + x ) × [tex](1+0.5)^{4}[/tex]

solve it we get

x = $4877.75

so money deposited after end of 3rd year is $4877.75