# Time Value of Money- Annuity

You plan to retire in twenty years. When you retire, you will need $150,000 per year for thirty years with the first payment needed at t=21. You expect to receive $50,000 from a trust at t=12 which you will deposit in your retirement account. At t=10, you plan to take a world cruise that will cost you $15,000 to be paid out of the retirement account. You plan to make nineteen equal yearly deposits beginning at the end of second year into this account. If the account pays interest at 10 percent p.a., what should be equal annual deposits?

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#### Solution Preview

Current time = t=0

To be received :

30 receipts from t= 21 to t= 50 of $150,000

At t= 10 , for world cruise $15,000

To be paid

At t= 12 $50,000 from another trust

19 deposits from t= 2 to t= 20 of x (to be calculated)

We will calculate the PV of deposits and receipts at time 0

The PV of deposits must equal PV of receipts

Receipts ...

#### Solution Summary

The solution calculates annuity as the time value of money.