Question

Using your Present Value for a Lump Sum, Present Value for an Annuity, Future Value of a Lump Sum and Future Value of an Annuity, create four separate problems (with solutions) that use each table. Therefore, you need one problem for each table but four problems in total. Please include formulas and explanations where needed.

The tables aren't provided because it is however you want to do it (however, it does include the period and interest rate).

(i.e) Can be up to 5 periods and 1%-12% of interest rate.

Answer 1

To calculate present value of a lump sum, we should use the Present Value of $1 table. For example, Olivia is interested in saving money for college and want to calculate how much she would need put in the bank today to return a sum of $40,000 in 5 years. The bank returns an interest rate of 3% per year during these 5 years. Looking at the PV table, n = 5 years and i = 3% returns a present value factor of 0.863. Multiplying this factor by the return amount of $40,000 produces $34520. This means she  would need to put in the bank now approximately $34520 to have $40,000 in 5

Annuities are a series of equal payments made over time, and ordinary annuities pay the equal installment at the end of each payment period within the series. This can help a business understand how their periodic returns translate into today’s value.

For example, assume that Sam needs to borrow money for college and anticipates that she will be able to repay the loan in $1,200 annual payments for each of 5 years. If the lender charges 5% per year for similar loans, how much cash would the bank be willing to lend Sam today? In this case, she would use the Present Value of an Ordinary Annuity table where n = 5 and i = 5%. This yields a present value factor of 4.329. The current value of the cash flow each period is calculated as 4.329 × $1,200 = $5,194.80. Therefore, Sam could borrow $5,194.80 now given the repayment parameters.

A lump sum payment is the present value of an investment when the return will occur at the end of the period in one installment. To determine this return, the Future Value of $1 table is used.

For example, Alex is saving for a vacation he plans to take in 4 years and want to know how much his initial savings will yield in the future. He  decides to place $4,500 in an investment account now that yields an anticipated annual return of 8%. Looking at the FV table, n = 4 years, and i = 8%, which return a future value factor of 1.360. Multiplying this factor by the initial investment amount of $4,500 produces $6120. This means his initial savings of $4,500 will be worth approximately $6120 in 4 years.

A future value ordinary annuity looks at the value of the current investment in the future, if periodic payments were made throughout the life of the series.

For example, Tiya is  saving for college trip and expect to contribute $10,000 per year for the next 3 years in an investment plan. The plan anticipates a periodic interest yield of 12%. How much would the investment be worth in the future meeting these criteria? In this case, you would use the Future Value of an Ordinary Annuity table. The relevant factor where n = 3 and i = 12% is 3.374. Multiplying the factor by the amount of the cash flow yields a future value of these installment savings of (3.374 × $10,000) $33740. Therefore, you could expect your investment to be worth $33740 at the end of 3 years, given the parameters.