Time Value of Money

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Lena decided to forego a lump sum savings plan where she puts in $50,000 today and gets back $70,000 in 5 year’s time. What is the opportunity cost (in % terms) of the $50,000 to Lena?

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6 months from now, Ravi would like to place $3000 into a fixed rate savings account which gives a quoted interest of 6% per year. The interest is paid out quarterly.

Assuming there are no other cashflows, how much will be in the account 2 years from today?

30 months ago, Desmond placed $1000 into an account which practises continuous compounding at a guaranteed rate of 8% per year. If he withdraws the full amount today, how much can he withdraw? (Round off to the nearest dollar)

A business owner estimates that her business will be worth $5 million in 4 years. What is the estimated value of her business today, assuming a discount rate of 15%?

Chen wants to have $100,000 in his daughter’s education account in 5 years. The account credits 6.5% interest on a continuous compounding basis. How much should he have in the account today to reach his target of $100,000 in 5 years?

An investment plan requires the investor to place $10,000 at the beginning of each year for 7 years. Assuming that the investment plan grows at 9% per year, how much is the estimated value at the end of 7 years?

Lilian opened a savings account 3 years ago, where she placed an initial deposit of $2000. She placed another $1000 the following year. The account credits daily interest at a quoted interest rate of 3.65% per year. How much is in her account today?

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Holmes is considering to buy an ordinary annuity that will provide him a yearly payment of $10,000 for the next 12 years. The rate of return of the annuity is quoted at 15% per year. How much is a reasonable price to pay for this annuity today?

Katie is retiring next month and she is presented with 2 options for her retirement package.

Option A: 15-year annuity due. Annual payments of $100,000.
Option B: Perpetuity with annual payments of $60,000.

Assuming a discount rate of 6%, which option has the greater present value to her?

A private wealth manager was tasked to source for an ordinary annuity that can provide his client with a fixed payment of at least $$300,000 payout per year for the next 10 years. The client is able to fork out $1.5 million for the annuity. What is the minimum rate of return that the ordinary annuity must have in order to meet the required payouts?