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Trent has opened an RRSP account by making an initial deposit of ​$900. He intends to make annual deposits for 26 years increasing at a constant rate of ​3.7%. How much of the accumulated value just after the last deposit was made is interest if interest is ​4.1% compounded anually​?

User AndW
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Answer: To solve this problem, we can use the formula for the future value of an annuity with increasing payments:

FV = (PMT x (((1 + r)^n) - 1) / r) + PV x (1 + r)^n

where FV is the future value, PMT is the periodic payment, r is the interest rate per period, n is the number of periods, and PV is the present value.

Using the given information:

PMT = the annual deposit increasing at a constant rate of 3.7%, so we can write it as PMT = 900 x (1 + 0.037)^t, where t is the number of years since the initial deposit.

r = 4.1% compounded annually, so we can write it as r = 0.041.

n = 26, since Trent makes annual deposits for 26 years.

PV = 900, since that was the initial deposit.

Plugging these values into the formula, we get:

FV = (PMT x (((1 + r)^n) - 1) / r) + PV x (1 + r)^n

FV = (900 x (1 + 0.037)^26 x (((1 + 0.041)^26) - 1) / 0.041) + 900 x (1 + 0.041)^26

FV = $53,610.60

To find the amount of accumulated value just after the last deposit was made that is interest, we need to subtract the total amount of deposits made over the 26 years from the final future value:

Interest = FV - (PMT x n) - PV

Interest = $53,610.60 - (900 x 26) - $900

Interest = $13,128.60

Therefore, the amount of the accumulated value just after the last deposit was made that is interest is $13,128.60.

Explanation:

User Sushim Mukul Dutta
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