Question

Dipper has a 10 year increasing annuity immediate that pays $100 at the end of the first year, $200 at the end of the second year, ... , and $1000 at the end of the 10th year. He exchanges the annuity for a perpetuity of equal value that pays X at the end of each year. If the effective annual interest rate is 3%, find the value of X

Answer 1

Hello Sir/ Mam

YOUR REQUIRED ANSWER IS $134.52

Dipper has 10 year increasing annuity immediate that pays $100 at the end of the first year, $200 at the end of the second year and so on uptill $1000 at the end of the 10th year.

He exchanges this annuity with perpetuity of equal value that pays X at the end of the each year. Effective Annual Interest Rate is 3%.

To calculate the value of X, we must compute the present value of annuity and perpetuity and equate the both cashflows.

Time	Cash Flows	Present Value Factor	Present Value
1	$100.00	0.970873786	$97.09
2	$200.00	0.942595909	$188.52
3	$300.00	0.915141659	$274.54
4	$400.00	0.888487048	$355.39
5	$500.00	0.862608784	$431.30
6	$600.00	0.837484257	$502.49
7	$700.00	0.813091511	$569.16
8	$800.00	0.789409234	$631.53
9	$900.00	0.766416732	$689.78
10	$1,000.00	0.744093915	$744.09
Total			$4,483.90

Hence,

Hence,

I hope this solves your doubt.

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