Pre calculus Finance and investing

Question

Bruce and Sharon are the same age and both had pension plans with their place of employment. Sharon started contributing $2500 per year at age 25. Bruce did not start making regular contributions until age 40, but at that point contributed $6500 per year. Sharon’s plan earned an annual rate of 4.55% compounded quarterly whereas Bruce’s plan paid an annual rate of 4.85% compounded semi-annually.

A. What was the value when each of them were 65 years old?

B. How much did Bruce and Sharon contribute to their respective plans?

C. How much interest did each earn?

D.Compare their rate of returns

Answer 1

Part A:

If you think of each individual deposit of money as an investment by itself, then an investment of

$ = A,

interest rate = r,

compounds per year = n

can be modeled exponentially like:

A * (1 + r/n)^(n * t)

where t is the number of years passed since investment

notice, for each subsequent investment, there will be one fewer year of interest

therefore we can write the sum of all the total investments after T years as:

sum(t = 0 -> t = T) [A * (1 + r/n)^(n * t)]

for Sharon, A = 2500, n = 4, T = 40, r = .0455

for Bruce, A = 6500, n = 2, T = 25, r = .0485

Part B:

Bruce contributes 6500$ for 25 years. Sharon contributes 2500$ for 40 years.

Part C:

Take their total value calculated in part A, and subtract the investments determined in part B to find their value gained through interest

Part D:

Rate of return is an extremely vague variable, and could mean a number of different things. In this case we will just guess that it means “find the average amount of interest earned per year”. To do this, take the interest calculated in part C, and divide by the total number of years each invested.