Jerry calculates that if he makes a deposit of $5 each month at an APR of 4.8%, then at the end of two years he'll have $100.

Question

Benny says that the correct amount is $135. The regular deposits rule of thumb should be helpful here.

Suppose the total amount deposited ($5 per month for two years) is instead put as a lump sum at the beginning of the two years as principal in an account earning an APR of 4.8%. Use the compound interest formula (with monthly compounding),
Balance after t periods = Principal × (1 + r)t,
to determine how much would be in the account after two years. Whose answer is ruled out by this calculation? Why?
Jerry's answer is ruled out by this calculation because the amount should be more than $132.07.
Both Benny and Jerry's answers are ruled out by this calculation because the amount should be greater than $135.01.
Benny's answer is ruled out by this calculation because the amount should be less than $132.07.
Benny's answer is ruled out by this calculation because the amount should be exactly $100.

 

I am so confused with this question. 

Answer 1

Over the two years, Jerry will have made 24 deposits of $5 for a total of 24*5 = $120.

 

If he had instead deposited the entire $120 at the beginning of the 2 years, he'll earn more interest than if he splits it up monthly.

 

If the yearly APR is 4.8%, then the monthly interest rate is 4.8%/12 = 0.4% = 0.004. He'll have invested it for 24 months, so

Maximum Balance = $120 (1.004)²⁴ = $132.07

 

This eliminates $135 as a possible amount, since it is more than what he would make with a single lump sum deposit.

 

Incidentally, Jerry's answer is also incorrect, since it is less than what he deposits. However, the questions asks "Whose answer is ruled out by this calculation?", and this specific calculation only eliminates Benny's answer.