Time value of money - investment

The time value of money is the value of a specific amount of money after a set length of time. Numerous investors profit from time value money when the fund’s worth rises during the investment period. But, in rare situations, the time value of money might decrease, and if the decrease is significant, investors may suffer significant losses.

Many factors influence the change in the temporal value of money. One factor is inflation, which causes the value of money to fall as a result of a weak currency. Inflation is an economic issue that can occur as a result of a large amount of money in circulation. Therefore, it is crucial to put into consideration the inflation rate while determining the time value of money so that the investors can know the actual return on their investments.

The other factor is the tax effect. Every government has its tax rate that is used in calculating the amount of tax that investors need to pay from their returns. Mostly, this tax rate is used by the investors also to determine the actual return that they receive. In the case of Bob and Lisa, the tax effects are assumed to be absent, and therefore their savings will earn interest without tax deduction. Again, the interest rate for each year is assumed to be free from inflation. In other words, it is assumed that the economy would be stable during the entire period of their savings (Patnaik, n.d.).

The kind of investment that Bob and Lisa engage is annuity since it entails an annual contribution to their saving plans. For Lisa, the number of contributions is 13 since the payments she made began from the first year of working. Therefore, to obtain her savings at age 32, the time value of money for each contribution need to be determined using as follows:

Future Value (FV) =2000(1+r)

n=13

r=0.07

FV=2000(1+0.07)=43,100.98

The money would then grow for another 33 years when she is 65. So, interest compounding would be used to calculate the time value of money at that age. Therefore;

Value at age 65=43,100.98 (1+0.07)33=401931.29 The IRA investment for Bob, on the other hand, is an annuity for the whole 33 years. This contribution is slightly different from the one for Lisa because he contributes for the entire period of investment, then he began to withdraw. Lisa just made 13 contributions and waited for the maturity date of 65 years. So, the time value of money for Bob would be calculated as follows:

Future Value (FV) =2000(1+r)

N=33

r=0.07

FV=2000(1+0.07) =254, 517.53

It can be seen that the future value of Lisa’s savings is higher than that of Bob. It is higher because her money grew for a longer period than the length of the period in which Bob’s savings grew. The first phase of growth of Lisa’s savings was 13 years of annuity payments and the second phase was 33 years which involved the compounding growth of the money that she had in her savings after she stopped the annual contributions.

The following is the Excel output that summarizes the details of the investments:

Lisa

Bob

Annual Contribution

2000

2000

Time

13

33

Return rate

7%

7%

Future value

$ 43,100.98

$ 254,517.53

Value at age 65

$ 401,931.24

$ 254,517.53

The future value in the table is the value of the savings after the period of contribution. The chart for future value and value at age 35 is as follows:

Where 1 is Lisa’s investment, and 2 is Bob’s investment

Reference

Patnaik, P. The value of money (1st ed.).