# \$1,100 per month for 10 years, if the account earns 2% per year

Discussion in 'Calculator Requests' started by math_celebrity, Oct 26, 2021.

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\$1,100 per month for 10 years, if the account earns 2% per year

What the student or parent is asking is: If they deposit \$1,100 per month in a savings/investment account every month for 10 years, and they earn 2% per year, how much will the account be worth after 10 years?

Deposits are monthly. But interest crediting is annual. What we want is to match the two based on interest crediting time, which is annual or yearly.
1100 per month. * 12 months in a year = 13,200 per year in deposit

Since we matched interest crediting period with deposits, we now want to know:
If they deposit \$13,200 per year in a savings/investment account every year for 10 years, and they earn 2% per year, how much will the account be worth after 10 years?

This is an annuity, which is a constant stream of payments with interest crediting at a certain period.

Calculate AV given i = 0.02, n = 10
AV = Payment * ((1 + i)^n - 1)/i

AV =13200 * ((1 + 0.02)^10 - 1)/0.02
AV =13200 * (1.02^10 - 1)/0.02
AV =13200 * (1.2189944199948 - 1)/0.02
AV =13200 * 0.21899441999476/0.02
AV = 2890.7263439308/0.02
AV = 144,536.32