Question

Q1

Frisco Hardware is trying to do some financial planning. The company knows it will need to have $423038 in 10 years to pay off a loan. The company will be receiving $75020 at the end of year 8 from a licensing deal with another manufacturer, but the company will have to make a large payment of $51455 at the end of year 5 to fund a retirement account for the CEO. How much should the company deposit today to meet all future obligations? Assume an interest rate of 7% compounded annually.

Enter your answer as: 1234

Round your answer. Do not use a dollar sign ("$"), any commas (",") or a decimal point (".").

Q2

You deposit $387 at the end of each month into an account that pays a nominal annual rate of 8% compounded monthly. How much will you have in the account at the end of 18 years?

Enter your answer as follows: 12345

Round your answer. Do not use a dollar sign ("$"), any commas (",") or a decimal point (".").

Answer 1

Part 1)

P = 423038(P/F, 7%, 10) + 51455(P/F, 7%, 5) – 75020

P = Amount that the company needs to deposit today to meet all the future obligations

P = 423038/(1 + 0.07)¹⁰ + 51455/(1 + 0.07)⁵ – 75020

P = (423038 × 0.5083) + (51455 × 0.7130) – 75020

P = 215030.22 + 36687.42 – 75020

P = 176698

Part 2)

No. of interest periods per year, (C) = 12

Effective interest rate (R) = ((1 + (i/C))^C – 1

R = ((1 + (8%/12))¹² – 1

R = 8.30% compounded annually

Amount deposited per month = 387. So annual amount deposited is 4644

The objective is to find the future worth of n equal payments which are made at the end of every interest period till the end of the nth interest period at an interest rate of i compounded at the end of each interest period.

F = A[((1 + i)ⁿ – 1)/i]

F = A(F/A, i, n)

(F/A, i, n) = Equal payment series compound amount factor

A = Equal amount deposited at the end of each interest period = 4644

n = Number of interest periods = 18

i = Interest rate = 8.30 or 0.083

F = Single future amount

F = 4644[((1 + 0.083)¹⁸ – 1)/0.083]

F = 4644(F/A, 8.30%, 18)

F = 4644[((1.083)¹⁸ – 1)/0.083]

F = 4644 × 37.560

F = 174427.42