How do I calculate a simple compound interest of Principal = £5,000, with monthly contributions of £75 over next 10 years with interest of 4% being applied annually?
+37091 The initial deposit will earn interest for ten years 5000(1.04)^10 = 7401.22 at the end
the payments will accumulate as follows
F=A[ (1+i)^n -1 ] / i where the period is 1/12th of a year (monthly periods) and inteest is 1/12 of 4% =.003333
75 (1.003333)^120 -1)/.003333 =$11043.50
TOTAL: 7401.22 + 11043.50 = $ 18,444.72 at the end of ten years
(I think)
EP: You made a small error in projecting the FV of 5,000 pounds. If you take the interest rate of 4% as "compounded monthly", then you have to project the FV at that rate. If you did that, then the FV of 5,000 pounds =7,454.16.
The FV of the payments is OK, so that the accurate FV of both should be:
7,454.16 + 11,043.74 =18,497.90 pounds.
However, the questioner says the "interest of 4% being applied ANNUALLY", which makes it sound that it is not compounded monthly, but annually. If that is the case, then the interest rate has to be converted from annual compound to monthly compound, which would come to 3.93% copounded monthly. This would only apply to the stream of 75-pound monthly payments. That would change the FV to =11,002.19 + 7,401.22=18,403.41.
Many thanks for your input here - but the question is based on annual, not monthly interest, and to include the principal (£5000) as well as the monthly payments. Also, how do work this out using a scientific calculator? - your help on this would be much appreciated.
Many thanks for your input here - but the question is based on annual, not monthly interest, and to include the principal (£5000) as well as the monthly payments. Also, how do work this out using a scientific calculator? - your help would be much appreciated.
You would combine 2 separate formulas and ADD up their results together:
1) For the 5,000 pounds, you use this formula:
FV =5,000 x [1 + 4%]^10
FV =5,000 x 1.04^10
FV =5,000 x 1.48024428491834392576
FV =7,401.22 Pounds
2) For the monthly payments of 75 pounds, you would use this formula. You still have to convert the interest rate from annual compound to monthly compound, which comes to 3.93% comp. monthly:
FV=P{[1 + R]^N - 1/ R}=FV OF $1 PER PERIOD.
FV =75 x {[1 + 3.93/1200]^(10x12) - 1} / 3.93/1200
FV =75 x {[1.003275]^120 - 1} / 0.003275
FV =75 x 146.70761
FV =11,003.07 Pounds
3) ADD 1 and 2 above together:
7,401.22 + 11,003.07 =18,404.29 - Pounds. The small differences of a few pennies is due to rounding off. Good luck to you.
