Since the amount is compounded monthly, the amount would triple after 26 months
Since the money is compounded monthly, we use the compound interest formula
How to calculate compound interest
The amount obtained on compound interest is given by A = P(1 + r)ⁿ where
- P = present value,
- r = interest rate and
- n = time
Now, since you deposit an amount of $1000 at an interest rate of 3.15 % per year compounded monthly and an extra $75 added monthly after n month, the amount is A = A' the amount compounded monthly + the extra amount monthly A"
Amount compounded monthly
Since A' = P(1 + r)ⁿ where
- P = initial amount = $1000,
- r = interest rate = 3.15 %/12 (since it is compounded monthly) = 0.002625 and n = number of months
So, A' = P(1 + r)ⁿ
= 1000(1 + 0.002625)ⁿ
= 1000(1.002625)ⁿ
Extra amount added monthly
Also, since $75 is added monthly, after n months, A" = 75n
Total amount after n months
So, the total amount added is A = A' + A"
= 1000(1.002625)ⁿ + 75n
Time for amount to triple
Since we require the time when the initial amount would triple, so, A = 3A'
= 3 × 1000
= 3000.
So,
A = 1000(1.002625)ⁿ + 75n
3000 = 1000(1.002625)ⁿ + 75n
3000 - 75n = 1000(1.002625)ⁿ
The solution of the above equation is obtained graphically. Find the graph in the attachment. They intersect at (25.736, 1069.797)
So, n = 25.736
≅ 26 months
So, the amount would triple after 26 months
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