Question

Marianne opened a retirement account that has an annual yield of 5.5%. She is planning to retire in 25 years. How much should she put into the account each month so that she will have $500,000 when she retires?

Answer 1

Monthly deposit, P = $776.41

Explanation:

Interest rate per annum = 5.5%

number of years = 25

Since she pays monthly, number of payments per annum = 12

Interest rate per period, r = (Interest rate per annum)/(number of payments per annum)

r = 5.5%/12 = 0.46%

Number of periods, n = number of years * number of payments per annum

n = 25 * 12 = 300

Future value of annuity, FVA = $500,000

Monthly deposit will be:

`P = ((FVA) * r)/((1+r)^(n) -1) \\P = ((500000) * 0.46/100)/((1+0.46/100)^(300)-1 )`

P = $776.41

Answer 2

MP = $778.77

she should put $778.77 into the account each month

Explanation:

This problem can be solved using the compound interest formula;

FV = MP{[(1+r/n)^(nt) - 1]/(r/n)} .......1

Where;

FV = Future value

MP = monthly contribution

r = yearly rate

n = number of times interest is compounded per year.

t = number of years

Given

FV = $500,000

t = 25 years

r = 5.5% = 0.055

n = 12 months/year

From equation 1, making MP the subject of formula;

MP = FV/{[(1+r/n)^(nt) - 1]/(r/n)}

Substituting the given values we have;

MP = 500,000/(((1+0.055/12)^(12×25) -1)/(0.055/12))

MP = $778.77

she should put $778.77 into the account each month