Question

Jack is 2 years old

Hes parents are saving to send him to a private school and need 140,000 when he is 15 years old

They currently have 20,000 in a fund at 7% per annum until he is 15 years old

They want to make monthly contributions to another account that pays 11% with annunal compunding.

What is the monthly contribution to reach 140k at 15 years old

Answer 1

Future Value:

Future Value is Value of current asset at future date grown at given int rate or growth rate.

FV = PV (1+r)^n
Where r is Int rate per period
n - No. of periods

FV of Annuity :

Annuity is series of cash flows that are deposited at regular intervals for specific period of time. Here deposits are made at the end of the period. FV of annuity is future value of cash flows deposited at regular intervals grown at specified int rate or Growth rate to future date.

FV of Annuity = CF [ (1+r)^n - 1 ] / r
r - Int rate per period
n - No. of periods

Amount Required after 13 Years ( 15 - 2) is $ 140000

FV of $ 20000 after 13 Years:

Particulars	Amount
Present Value	$           20,000.00
Int Rate	7.0000%
Periods	13

Future Value = Present Value * ( 1 + r )^n
= $ 20000 ( 1 + 0.07) ^ 13
= $ 20000 ( 1.07 ^ 13)
= $ 20000 * 2.4098
= $ 48196.9
FV of annuity shall be 140000 - 48196.90

= $ 91803.10

Monthly Int rate:Particulars

Monthly Rate = [ ( 1 + r )^ ( 1 / n ) - 1 ]
r = Effective Annual Rate
n = No. of times compounded per anum

n = 12

= [ [ ( 1 + EAR )^( 1 / n ) ] - 1 ]
= [ [ ( 1 + 0.11 )^( 1 / 12 ) ] - 1 ]

= [ [ ( 1.11 )^( 1 / 12 ) ] - 1 ]
= [ [ 1.0087 ] - 1 ]
= [ 0.008699
= 0.87%
Monthly deposit calculation:

Particulars	Amount
FV of Annuity	$         91,803.10
Int Rate	0.8700%
Periods	156

FV of Annuity = Cash Flow * [ [(1+r)^n ] - 1 ] /r
$91803.1 = Cash Flow * [ [ ( 1 + 0.0087 ) ^ 156 ] - 1 ] / 0.0087
$91803.1 = Cash Flow * [ [ ( 1.0087 ) ^ 156 ] - 1 ] / 0.0087
$91803.1 = Cash Flow * [ [ ( 3.8626 ] - 1 ] / 0.0087
$91803.1 = Cash Flow * [ 2.8626 ] / 0.0087
Cash Flow = $ 91803.1 * 0.0087 / 2.8626
Cash Flow = $ 279.01
Monthly deposit required is 279.01