uncle Fraser needs at the end of 10 years $35000 and his only investment outlet is an 8 percent long-term certificate of deposit (compounded annually). With the certificate of deposit, uncle fraser makes an initial investment at the beginning of the first year.
a. What single payment could he make at the beginning of the first year to achieve this objective?
b. And if uncle Fraser were to make an investment at the end of each year annually for 10 years, what amount would he need to invest every year to achieve this objective?
| (a) | Let the amount be A - | ||||
| A x (1+r)^n = | 35000 | ||||
| A x (1.08)^9 = | 35000 | ||||
| (There will be no compounding for the 1st year as the payment is made at the end of year 1) | |||||
| A = | 35000/1.08^9 | ||||
| A = | 17508.71 | ||||
| (b) | Let the amount be A - | ||||
| A x(1.08)^9 + A x (1.08)^8 +…..+A x (1.08)^0 = | 35000 | ||||
| A x (1.08^9 + 1.08^8+….+1.08^0) = | 35000 | ||||
| A x 14.4865 = | 35000 | ||||
| A = | 35000/14.4865 | ||||
| A = | 2416.032104 | ||||
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