Question

Kate deposits $50,000 at the end of each year for exactly 20 years, in an account paying annual interest of 5%. The first payment will occur in exactly 1 year. Draw timelines.

(i) How much will she have in deposit after 20 years?

(ii) If Kate instead deposited $5,000 at the end of each month, how much will she have on deposit after 20 years? The first payment will occur in exactly 1 month.

Answer 1

i) We are given the following information:

PMT	$            50,000.00
r	5.00%
n	20

We need to solve the following equation to arrive at the required FV

FV = PMT X (1+r)" – 1 (1 +0.05)20 – 1 FV = PMTX 0.05 FV = 1,653, 297.71

So the Account will have $1,653,297.71 accumulated in it at the end of year 20

Timeline 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 1 2 3 4 5 6 7 8 9 16 17 18 19 20 10 11 12 13 14 15 IPMT

The 50 represents 50000, and the shorthand is used for visibility in the image

ii)We are given the following information:

PMT	$              5,000.00
r	5.00%
n	20
Frequency	12

We need to solve the following equation to arrive at the required FV:

(1+ )nx Frequency - 1 FV = PMT X- Frequency (1 + 0.05 )20x12 - 1 FV = PMTX 0.05 FV = 2,055, 168.34

So the account will have $2,055,168.34 accumulated in it