Question

If you invest in gold bars for your savings at a cost of $25,000 and after 8 years its future value is $53,589.72, What is the interest annual interest rate earned for this investment? What is the equivalent annuity savings amount of this investment: annually and monthly? Annually- Monthly-

Answer 1

(1)

If annual interest rate be r%, then

$25,000 x (1 + r)⁸ = $53,589.72

(1 + r)⁸ = 2.1436

Taking 8th root,

1 + r = 1.1

r = 0.1 = 10%

(2)

(i) If annual saving be S, then

S x P/A(10%, 8) = $25,000

S x 5.3349** = $25,000

S = $4,686.12

(ii) Monthly nominal interest rate = 10%/12 = 0.83% and number of months in 8 years = 8 x 12 = 96.

If monthly savings be S, then

S x P/A(0.83%, 96) = $25,000

S x 65.9935** = $25,000

S = $378.83

**P/A(10%, 8) = [1 - (1.1)^-8] / 0.1 = (1 - 0.4665) / 0.1 = 0.5335 / 0.1 = 5.3349

**P/A(0.83%, 96) = [1 - (1.0083)^-96] / 0.1 = (1 - 0.4523) / 0.0083 = 0.5477 / 0.0083 = 65.9935