Question

Rhoda is saving money to take a trip to Egypt 3 years from today.The trip currently costs 2800 but cost is expected to increase at an annual inflation rate of 4 %. If Rhoda has a current balance of 600 in her saving account and the the account earns interest 6% convertible quarterly, what level amount should she deposit at the beginnig of ecah month in order to have the amount needed for the trip at the end of 3 years ?

Answer 1

Expected cost of the trip at the end of 3 years = from today = 2,800*1.04^3

= 2,800 * 1.124864

= $3,149.62

.

Current Balance in Saving Account = $600

Interest rate convertible quarterly = 6%

Quarterly interest rate = 6%/4 = 1.5%

Monthly interest rate = 6%/12 = 0.5%

.

Future value of the Current Balance in Saving Account of $600

= 600*1.015^(3*4)

= 600*1.005^12

= 600*1.195618

= $717.371

.

.

Balance amount required for the trip = $3,149.62 - $717.371

= $2,432.248

.

.

Let the level amount that Rhoda should deposit at the beginnig of each month in order to have the amount needed for the trip at the end of 3 years be x

.

Therefore,

(1.005^36 - 1)x + x*FVIFA(0.5%,36) = 2,432.248

(1.196681 - 1)*x + 38.1454x = 2,432.248

0.196681x + 38.1454x  = 2,432.248

39.53278x  = 2,432.248

x = 2,432.248/39.53278

x = 61.53

.

.

So level amount that Rhoda deposit at the beginnig of ecah month in order to have the amount needed for the trip at the end of 3 years is $61.53 each month.

.

So , out of the given options, Option-e: $61.55 is the correct answer.