Gavin is 15 and works after school washing dishes in a resturaunat. He has decided to invest $50 per week. He is investing in a fund that has an 8% interest rate, with interest COMPOUNDED MONTHLY.
In TVM solver terms, the present value = 0 The amount of the regular deposit is the payment. P/Y is the number of payments (I.e., deposits) made in 1 year. N is the total of payments that are made.
Each Payment is made at the beginning of each month. Solve for the future value.
Number of weeks in 2 years = 104
I for Interest = 8%
PV= 0
PMT = each amount of each deposit = 50$
FV = leave at 0 for now
P/Y= the number of deposits in 1 year = 52
C/Y = 12 Compounded Monthly
Gavin is 15 and works after school washing dishes in a resturaunat. He has decided to invest $50 per week. He is investing in a fund that has an 8% interest rate, with interest COMPOUNDED MONTHLY.
In TVM solver terms, the present value = 0 The amount of the regular deposit is the payment. P/Y is the number of payments (I.e., deposits) made in 1 year. N is the total of payments that are made.
Each Payment is made at the beginning of each month. Solve for the future value.
✅ Answers
? Best Answer
Each payment of $50 is multiplied by (1+0.08/12)=(151/150) for each month.
So a payment invested for “n” months attains a value of $50(151/150)ⁿ.
After a period of “Y” years, the last payment was invested for 1 month, the previous payment for 2 months, et cetera. The first payment was invested for a total of (12Y) months. Hence the total value of the investment is the geometric sum:
Σ $50(151/150)ⁿ , summed from n=1 to n=12Y.
The standard geometric series formula reduces that sum to:
$7550 × { (151/150)^(12Y) – 1 }
No point in doing that silly TVM solver stuff here. Just use your junior high school algebra.