P5-18 Calculating deposit needed. You put $10,000 in an account earning 5%. After 3 years, you make another deposit into the same account. Four years later (7 years after your original $10,000 deposit), the account balance is $20,000. What was the amount of the deposit at the end of year 3

$4877.80

Explanation:

The computation of amount of the deposit at the end of year 3 is shown below:-

Future value = Present value × (1 + Rate of interest ÷ 100)^number of years

$20,000 = 10,000 × (1 + 5 ÷ 100)^7 + Deposit at end of year 3 × (1 + 5 ÷ 100)^4

$20,000 = 10,000 × (1.05)^7 + Deposit at end of year 3 × (1.05)^4

$20,000 = 14071.00423  + Deposit at end of year 3 × (1.05)^4

Deposit at end of year 3 = ($20,000 - 14071.00423 ) ÷ (1.05)^4

= $5928.995773  ÷ 1.21550625

= $4877.799496

or

= $4,877.80

We simply applied the above formula to find out the amount of deposit at the year 3 end

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