Graham plans to save $100 each month for the next 20 years so he can purchase...

Graham plans to save $100 each month for the next 20 years so he can purchase a boat. If he earns 10% interest annually with monthly compounding, how much money will he have at the end of 20 years if he starts saving today?

Solutions

Expert Solution

Monthly interest rate = 0.83333% per month

Time = 12* 20 = 240 months

The future value of annuity due formula is used to calculate the ending value of a series of payments or cash flows where the first payment is received immediately. The first cash flow received immediately is what distinguishes an annuity due from an ordinary annuity.

FV of annuity due = (1 + i) * P [{(1 + i) ^n -1}/i]

Where,

Periodic deposit (P) = $100

Interest rate = 0.0083333

Time (n) = 240

Let's put all the values in the formula to solve for FV of annuity due

FV of annuity due = (1 + 0.0083333) * 100 [{(1 + 0.0083333) ^240- 1}/ 0.0083333]

= (1.0083333) * 100 [{(1.0083333) ^240- 1}/ 0.0083333]

= 100.83333 *[7.32801549339119- 1/ 0.0083333]

= 100.83333 *[6.32801549339119/ 0.0083333]

= 100.83333 * 759.36489666653

= 76569.29

So the amount he will have after 20 years is $76569.29

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Feel free to comment if you need further assistance J

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jeff jeffy answered 1 year ago

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