You are considering two savings options. Both options offer a rate of return of 7.6 percent. The first option is to save $2,500, $2,500, and $3,000 at the end of each year for the next three years, respectively. The other option is to save one lump sum amount today. You want to have the same balance in your savings account at the end of the three years, regardless of the savings method you select. If you select the lump sum method, how much do you need to save today?

Explanation: This question requires that the principle amount be calculated. This is the current value of the lump sum saving on the first day, before interest has been compounded. In essence this is the original savings value. To calculate this value, the compound interest formula can be used. However this formula needs to be manipulated so that the principal value, P, is determined:

P = [tex]\frac{A}{(1 + i)^{n} }[/tex]

Where:

P = Principal value: the original value of the saving on the first day, before interest has been taken into account.

A = Amount: The amount at the end of a specific period.

i = Rate of return: the profit, expressed as a an interest rate, that the savings earns periodically.

n = The amount of time that the savings is invested for.

When this formula is applied then the following answer is computed:

P = [tex][\frac{2,500}{(1 + 0.076)^{1} }] + [\frac{2,500}{(1 + 0.076)^{2} }] + [\frac{3,000}{(1 + 0.076)^{3} }][/tex]

= $6 890,887434

Rounded off to $6,891

WeAreHelping WeAreHelping · Answer 2 · 2025-04-08T06:55:23-04:00

P = (2,500 / (1 + 0.076) ^ [1]) + (2,500 / (1 + 0.076) ^ [2]) + (3,000 / (1 + 0.076) ^ [3])

= $ 6 890,887434

Further Explanation

In the world of capital markets, investment in the future is known as Lump Sum (LS) investment. While investing regularly, also known as (Dollar) Cost Averaging (CA) or auto-debit. Provisions in each company can be different, but if Panin Asset Management has a monthly period of at least 1 year.

For more details, suppose you have $ 12,000. If invested with the LS method, assuming a return of 20%, and a period of 1 year, then at the end of the first year the value of money will develop to $ 14,400 (12,000 x 20% + 12,000).

Mathematically, assuming equity funds are able to provide a return rate of 20% per year, it is certain that the LS method is better than CA. Because with the LS method, all funds entered since the first time directly get 20% profit. If with the CA method, only the first deposit gets a 20% return, the rest because it is entered later gets a lower profit rate.

Lump-Sum

That is, official travel money is given at the beginning or before the employee departs on duty. The amount given is the entire expenditure projection during service or pre-calculated amount.

Reimbursement

That is, official travel money is given by way of replacement after the employee completes his service. Thus, all expenses during the trip are issued by the employees themselves and then replaced by the company based on the evidence related expenses.

Learn More

Lump-Sum https://brainly.com/question/13450926

Cost Averaging https://brainly.com/question/13450926

Details

Grade: College

Subject: Business

Keyword: lump-sum, cost, reimbursement