Two people want to take a trip to Nepal in two years. They set up a sinking fund at 6% interest. What will the monthly deposit be if they want the funds value to be 20,000 in two years. The account is an ordinary annuity.

Printable View

- May 4th 2006, 07:10 AMd.darbyshireFinance
Two people want to take a trip to Nepal in two years. They set up a sinking fund at 6% interest. What will the monthly deposit be if they want the funds value to be 20,000 in two years. The account is an ordinary annuity.

- Sep 13th 2006, 11:34 AMsonyAccumulation of annuityQuote:

Two people want to take a trip to Nepal in two years. They set up a sinking fund at 6% interest. What will the monthly deposit be if they want the funds value to be 20,000 in two years. The account is an ordinary annuity.

The way i will approach this problem is to first find the present value of the 20000 and then equate that to the present value of the annuity. I will work in periods of one month.

Let i be the effective rate of interest per month: i = (1.06)^(1/12) - 1 = 0.04867551

Hence the present value of the 20000 is = 20000(1+i)^(-24) = 17799.9288

You should be aware of the formula for the present value of an annuity payable in advance, that is: Installment * (1 - (1+i)^(-n)) / (i/(1+i)) where n is the number of installments.

now equate the present value of the annuity with the present value of the 20000 and solve for the installment:

17799.9288 = Installment * (1 - (1+i)^(-24)) / (i/(1+i)) = Installment * 22.70937022

=> Installment = 783.8142856

I hope this is helpful to you, please let me know if I should change my assumptions and revise the post accordingly. - Sep 13th 2006, 03:14 PMSoroban
Hello, d.darbyshire!

Quote:

Two people want to take a trip to Nepal in two years.

They set up a sinking fund at 6% interest.

What will the monthly deposit be if they want the funds value to be $20,000 in two years?

The account is an ordinary annuity.

You are expected to know the Annuity Formula:Code:`(1 + i)^n - 1`

A = D -------------

i

where*D*is the periodic deposit,*i*is the periodic interest rate,

. .*n*is the number of periods, and*A*is the final value.

Your problem has: .*i = 0.005, n = 24,*and*A = 20,000.*

Solve for*D.*