Question

please explain the answer step by step

$10,000 is invested with two schemes for 6 years:

1. into a saving account of nominal annual interest rate of 12% compounded monthly.

2. you use this 10,000 to purchase a 6 payment level annuity due at rate 10% and invest this payment into a saving account right after receiving them which pay annual effective interest of 6%.

which schema is more profitable ?

Answer 1

Option 1 Deposit in Saving account

Amount = 10000, Rate = 12/12= 1% per month,No of periods=6x12= 72 Calculate the Future Value

PV(1+r)ⁿ = FV

=10000(1.01)⁷²

=10000 x 2.0470993

=20470.993

Option 2 Purchase Annuity and deposit the payments into saving account.

1. calculate the Annuity

PV= Annuity + Annuity x Cumulative discounting value @10% for 5 years

10000 = Annuity + Annuity x 3.790786

10000 = Annuity(1 + 3.790786)

Annuity = 10000/ 4.790786

Annuity = 2087.34

2. Calculate the Fv of this annuity deposit @6%

Year End	Annuity	FV Factor	Amount
0	2087.34	1.41852	2960.9317
1	2087.34	1.33823	2793.3318
2	2087.34	1.26248	2635.2187
3	2087.34	1.19102	2486.0553
4	2087.34	1.12360	2345.3352
5	2087.34	1.06000	2212.5804
		Future Value	15433.4531

So It is clear from above that FV is more in option 1 so Opt for Depsoit in saving account .