Answer to Question #95193 in Financial Math for may

Question

Determine an interest rate less than 15%, a period of investment greater than two years, and a regular payment that will result in the total amount of interest you earn being equal to the total amount of money you put in? (for example, under what conditions will you have a future value of $1 000 000, having earned $500 000 interest?)

Answer 1

In essence, it is necessary to determine what is the relationship between time and the interest rate for money in order to double.

accrual rate = 2 (double) from the condition

Accordingly, accrual rate = (1 + r) ^ n = 2

choose any n> 2, and then we can find r

choose any r <.15, and then we can find n

For example, if r = .12 or 12%

1.12 ^ n = 2

n = log2 / log1.12 = 6.11 or about 6 years

When using the compound interest formula, we get:

FV = PV(1 + r) ^ n

1,000,000 = PV x 2

PV = 1,000,000 / 2 = $500,000

 interest = 1,000,000 - 500,000 = $500,000

provided that r =12% and n = 6 years

Regular Payment for an ordinary annuity when FV is known:

Pmt = FV / [((1 + r) ^ n - 1) / r]

Pmt = 1,000,000 / [1.12^6- 1) / 0.12] = $123,225.7