Question

Stacy would like to have $1,000,000 available when she retires in 30 years. If she can get an 11% return, what does she have to invest each month to achieve this goal?

Ronnie wants to give his grandson $10,000 on his 18th birthday. How much does he need to invest (5%) at the time his grandson is born to reach this amount?

Answer 1

1.

Amount to be paid by Stacy at the end of each month is $356.57

Information given:

Future value = $ 1,000,000

Number of years = 30

Interest rate = 11%

CALCULATIONS:

FV A = A * {(1 + r) n - 1} / r

Here,

FV A = $1,000,000

r = 11% / 12 = .9167% quarterly

n = 30 * 12 = 360 periods

A = ?

By substituting the values in the equation we get,

$1,000,000 = A * {(1+.00916666)360 - 1} / .00916666

$1,000,000 = A * (1.00916666360 - 1} / .00916666

$1,000,000 = A * 25.70809694/ .00916666

$1,000,000 = A * 2,804.519

A =$1,000,000 / 2,804.519

A = $356.57

2.

Amount to be invested by Ronnie at the time of his grandson’s birth is $4155.21

Information given:

Future value = $ 10,000

Number of years = 18

Interest rate = 5%

CALCULATIONS:

PV = FV * 1 / (1 + r) n

Here,

FV = $10,000

r = 5%

n = 18

PV = ?

By substituting the values in the equation we get,

PV = $10,000 * 1 / (1+.05)18

PV = $10,000 * 1 /(1.05)18

PV = $10,000 * .415521

PV = $4155.21