A local offers loans at 10% compounded quarterly. What effective annual interest

Question

A local offers loans at 10% compounded quarterly. What effective annual interest rate is being charged? What is the effective interest rate per quarter? A Trust Co. offers an RRSP program that guarantees a 14% annual compound rate of return for a 3-year period. However, the Trust Co. charges an annual (end-of-year) administration fee of $66.25. A minimum deposit of $2,000 is required, the amount you plan on depositing. As an alternative you are considering another RRSP plan that guarantees a 12% annual compound return for a 3-year period, has no admin or other fees and also requires a minimum $2,000 deposit. Which plan will provide you with the most money at the end. of 3 years and what are those amounts? What is the effective annual return being earned on the first RRSP plan?

Explanation / Answer

a) 10% per annum compounded quaterly. so the interest rate per quarter will be 2.5%
Compound intrest is calculating intrest on intrest so for
   first 3 months it is 2.5%
   nxt 3 months it will be 2.5% + 2.5% of 2.5% = 2.5625%
   nxt 3 months it will be 2.5625% + 2.5% of 2.5625% = 2.640%
  last 3 months it will be2.640% + 2.5% of 2.640% = 2.706%
so the effective intrest will be sum of all quarters which is equal to 2.5 + 2.5625 + 2.640 + 2.706 = 10.4085%

b) i) The deposit is 2000$
   so first year the intrest is 14% so 14%of 2000 = 280$
The admin fee is 66.25$
The final amount with scheme for first year will be 2000 + 280 - 66.25 = 2213.75

For the 2nd year the intrest will be on 2213.75
it is equal to 14% of 2213.75 = 309.925
the total amount for 2nd year will be 2213.75 + 309.925 - 66.25 = 2457.425

for 3rd year the interst will be on 2457.425 so 14% of 2457.425 = 344.039
so total amount on 3rd year will be 2457.425 + 344.039 - 66.25 = 2735.214

now the 12% plan will give you for the first year on 2000 is
2000 + 12% of 2000 = 2000 + 240 = 2240

in 2nd year intrest will be on 2240 so the amount is
2240 + 12% of 2240 = 2508.8

in 3rd year the amount is
2508.8 + 12% of 2508.8 = 2809.856

the first plan gives 2735.214 while 2nd plan gives 2809.856. so 2nd scheme gives most money

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